Muḥammad has absolutely no role in Christianity, and there is no explicit mention of him in the Christian Bible.
The first παράκλητος ("Comforter") was the Lord Jesus Christ.
In 1 John 2:1, it is written,
1 My little children, I write these things to you so that you do not sin. And if anyone sins, we have a comforter with the Father, Jesus Christ the righteous.
Αʹ Τεκνία μου ταῦτα γράφω ὑμῖν ἵνα μὴ ἁμάρτητε καὶ ἐάν τις ἁμάρτῃ παράκλητον ἔχομεν πρὸς τὸν πατέρα Ἰησοῦν Χριστὸν δίκαιον (TR, 1550)
Furthermore, the Lord Jesus Christ mentions ἄλλον παράκλητον ("another Comforter").
In John 14:16-17, it is written,
16 And I shall ask the Father, and He shall give you another Comforter, so that he may dwell with you forever, 17 the Spirit of truth, whom the world cannot receive, because it does not see him, neither does it know him, but you know him, for he dwells with you, and he shall be in you.
ΙϚʹ καὶ ἐγὼ ἐρωτήσω τὸν πατέρα καὶ ἄλλον παράκλητον δώσει ὑμῖν ἵνα μένῃ μεθ᾽ ὑμῶν εἰς τὸν αἰῶνα ΙΖʹ τὸ πνεῦμα τῆς ἀληθείας ὃ ὁ κόσμος οὐ δύναται λαβεῖν ὅτι οὐ θεωρεῖ αὐτὸ οὐδὲ γινώσκει αὐτό ὑμεῖς δὲ γινώσκετε αὐτὸ ὅτι παρ᾽ ὑμῖν μένει καὶ ἐν ὑμῖν ἔσται (TR, 1550)
The Greek word ἄλλον ("another") implies that there is an original Comforter. As mentioned, the original Comforter is the Lord Jesus Christ. The one who is "another Comforter" is the Holy Spirit.
In his commentary on 1 John 2:1, Henry Alford wrote,
There is no discrepancy between this passage [1 John 2:1], where the Son is our παράκλητος, and John 14:16, where the Holy Spirit is called by the same name: rather is there the closest accordance, seeing that there our Lord says He will pray the Father and He will send us ἄλλον παράκλητον: Himself, the Son of God, being thus asserted to hold this office in the first place, and the Holy Spirit to be His Substitute in His absence.
In addition, regarding the Spirit of truth, the Lord Jesus Christ told the apostles that (John 14:17) "he dwells with you, and he shall be in you" (παρ᾽ ὑμῖν μένει καὶ ἐν ὑμῖν ἔσται). The Greek verb μένει, translated as "dwells," is conjugated in the present tense, meaning that the Spirit of truth was dwelling with the apostles, right then, and right there, in the present. Muḥammad was not born for another 500-600 years. Therefore, Muḥammad could not be the other Comforter, the Spirit of truth. In addition, even Muslims would never admit that Muḥammad is actually in them. On the other hand, the Holy Spirit dwells in Christians (cp. 2 Tim. 1:14).
The reason that the Spirit of truth was dwelling with the apostles in the present, although the Holy Spirit would not be given until Pentecost (cp. Acts 2:4), is because the Holy Spirit is also the Spirit of the Son, Jesus Christ (cp. Rom. 8:9). The Lord Jesus Christ was dwelling with the apostles, and there exists a divine community between the Father, the Son, and the Holy Spirit --- the Holy Trinity.
The Prophecy of Joel
Many Muslims assert that the Holy Spirit cannot be the "Spirit of truth" or the "Comforter" because the Holy Spirit had always been with the faithful. However, there is no evidence that everyone who had faith in God prior to Pentecost possessed the Holy Spirit. Rather, God gave the Holy Spirit to whom He willed.
The prophet Joel prophesied of a time when God would pour out His Spirit (i.e., the Holy Spirit) upon all flesh, meaning both Jews and Gentiles, bondmen and freemen, men and women, children and adults, rather than upon select individuals. Logically, if God would in the future pour out His Spirit upon all flesh, then it had not been done so prior to that time.
In Joel 2:28-29, it is written,
28 And it shall come to pass afterwards, I will pour out My Spirit upon all flesh, and your sons and your daughters shall prophesy, your old men shall dream dreams, your young men shall see visions. 29 And in those days, I shall also pour out My Spirit upon the servants and upon the handmaids.
כח וְהָיָ֣ה אַֽחֲרֵי־כֵ֗ן אֶשְׁפֹּ֤וךְ אֶת־רוּחִי֙ עַל־כָּל־בָּשָׂ֔ר וְנִבְּא֖וּ בְּנֵיכֶ֣ם וּבְנֹֽותֵיכֶ֑ם זִקְנֵיכֶם֙ חֲלֹמֹ֣ות יַחֲלֹמ֔וּן בַּח֣וּרֵיכֶ֔ם חֶזְיֹנֹ֖ות יִרְאֽוּ׃ כט וְגַ֥ם עַל־הָֽעֲבָדִ֖ים וְעַל־הַשְּׁפָחֹ֑ות בַּיָּמִ֣ים הָהֵ֔מָּה אֶשְׁפֹּ֖וךְ אֶת־רוּחִֽי׃ (WLC)
In the New Testament, the apostle Peter confirms that this event occurred at Pentecost.
1 And when the day of Pentecost was fully come, they were all of one accord in one place.
4 And they were all filled with the Holy Spirit, and they began to speak with other tongues, as the Spirit gave them utterance.
16 But this is that which was spoken by the prophet Joel, 17 "And it shall come to pass in the last days," said God, "I will pour out of My Spirit upon all flesh, and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams. 18 And in those days, I shall pour out My Spirit upon My servants and upon My handmaidens, and they shall prophesy.
The Inadequacy of any Future Revelation
If indeed the Lord Jesus Christ is God as the majority of Christianity confesses, then any future revelation is inadequate compared to the revelation which came from the Lord Jesus Christ, God incarnate.
The reason is simple. A messenger is sent by, and delivers a message or revelation on behalf of, someone greater in authority. In the case of Moses, a man, he was sent by Yahveh, God, to deliver Yahveh's message and revelation to the people of Israel (cp. Exo. 3:15). However, because Moses was a man, this left open the possibility that someone "greater than Moses" (i.e., a greater man) could come thereafter to deliver another message or revelation on behalf of Yahveh to the people of Israel. Of course, the one "greater than Moses" was the Lord Jesus Christ (cp. Heb. 3:3).
Had the Lord Jesus Christ been just a man, the possibility would then exist that someone "greater than Jesus" could come after him with another message or revelation on behalf of Yahveh to the people of Israel. But, because the Lord Jesus Christ is God incarnate, no later message or revelation from someone who is just a man can supercede the message and revelation given by the Lord Jesus Christ, God the Son, on behalf of God the Father.
Since Muḥammad is just a man, and in addition, he claimed to have received the Qurʿān, not directly from God, but from the angel Gabriel, his message and revelation can in no way supersede that of the Gospel delivered by the Lord Jesus Christ, God incarnate, who spoke only what God the Father gave him to speak (cp. John 12:50).
A Contrary Gospel
There is one more thought that I feel is necessary to include. In his epistle to the Gal. 1:8-9, the apostle Paul wrote,
8 But if we, or an angel from heaven, preach [a gospel] to you other than what we have preached to you, let him be anathema! 9 As we said before, so now I say again --- if anyone preaches [a gospel] other than what you have received, let him be anathema!
Ηʹ ἀλλὰ καὶ ἐὰν ἡμεῖς ἢ ἄγγελος ἐξ οὐρανοῦ εὐαγγελίζηται ὑμῖν παρ᾽ ὃ εὐηγγελισάμεθα ὑμῖν ἀνάθεμα ἔστω Θʹ ὡς προειρήκαμεν καὶ ἄρτι πάλιν λέγω εἴ τις ὑμᾶς εὐαγγελίζεται παρ᾽ ὃ παρελάβετε ἀνάθεμα ἔστω (TR, 1550)
Since the revelation of Muḥammad which he claimed to have received from an angel contradicts the Gospel of the Lord Jesus Christ that was later preached by the apostle Paul and the other apostles, Muḥammad is considered anathema, or "accursed."
Alford, Henry. The Greek Testament, Vol 1. Boston: Lee and Shepard, 1874.