Is there any Scriptural support for claims about Jesus appearing to Muslims in dreams and visions?
Just as Lesley mentioned in her excellent response that ”nowhere in the Bible will you read of any prophecy about Jesus appearing to Muslims in dreams and visions. Perhaps that’s because Islam (and Muslims) did not exist till the 7th century.”
Nevertheless the Holy Spirit can operate in ways we find hard to understand. Remember that the high priest Caiaphas unwittingly prophesied about the death of Our Saviour:
“He did not say this on his own, but since he was high priest for that year, he prophesied that Jesus was going to die for the nation, and not only for the nation, but also to gather into one the dispersed children of God.”
God can work wonders though any person he chooses. Equally visions of Jesus can be had by believers or unbelievers alike.
Acts 2:17 tells to us that in the end days young men will see visions. Once again the Holy Spirit may possibly choose to lead some to the truth of Jesus Christ through these.
"'In the last days, God says, I will pour out my Spirit on all people. Your sons and daughters will prophesy, your young men will see visions, your old men will dream dreams.”
And again we may see the Jesus spoke to St. Paul as was on his way to Damascus and which eventually lead to his conversion, so we see that God’s ways are often mysterious and well above our thinking. If Jesus could appear to Saul, then he could do it to any unbeliever, including a Muslim!
Acts of the Apostles
Acts of the Apostles discusses Paul's conversion experience at three different points in the text, in far more detail than in the accounts in Paul's letters. The Book of Acts says that Paul was on his way from Jerusalem to Syrian Damascus with a mandate issued by the High Priest to seek out and arrest followers of Jesus, with the intention of returning them to Jerusalem as prisoners for questioning and possible execution.4 The journey is interrupted when Paul sees a blinding light, and communicates directly with a divine voice.
Acts 9 tells the story as a third-person narrative:
As he neared Damascus on his journey, suddenly a light from heaven flashed around him. He fell to the ground and heard a voice say to him, "Saul, Saul, why do you persecute me?"
"Who are you, Lord?" Saul asked.
"I am Jesus, whom you are persecuting," he replied. "Now get up and go into the city, and you will be told what you must do."
The men traveling with Saul stood there speechless; they heard the sound but did not see anyone. Paul got up from the ground, but when he opened his eyes he could see nothing. So they led him by the hand into Damascus. For three days he was blind, and did not eat or drink anything. — Acts 9:3–9, NIV
The account continues with a description of Ananias of Damascus receiving a divine revelation instructing him to visit Saul at the house of Judas on the Street Called Straight and there lay hands on him to restore his sight (the house of Judas is traditionally believed to have been near the west end of the street). Ananias is initially reluctant, having heard about Saul's persecution, but obeys the divine command:
Then Ananias went to the house and entered it. Placing his hands on Saul, he said, "Brother Saul, the Lord—Jesus, who appeared to you on the road as you were coming here—has sent me so that you may see again and be filled with the Holy Spirit." Immediately, something like scales fell from Saul’s eyes, and he could see again. He got up and was baptized, and after taking some food, he regained his strength. — Acts 9:13–19, NIV
Acts' second telling of Paul's conversion occurs in a speech Paul gives when he is arrested in Jerusalem.[Acts 22:6–21] Paul addresses the crowd and tells them of his conversion, with a description essentially the same as that in Acts 9, but with slight differences. For example, Acts 9:7 notes that Paul's companions did not see who he was speaking to, while Acts 22:9 indicates that they did share in seeing the light (see also Differences between the accounts, below). This speech was most likely originally in Aramaic (see also Aramaic of Jesus), with the passage here being a Greek translation and summary. The speech is clearly tailored for its Jewish audience, with stress being placed in Acts 22:12 on Ananias's good reputation among Jews in Damascus, rather than on his Christianity.
Acts' third discussion of Paul's conversion occurs when Paul addresses King Agrippa, defending himself against the accusations of antinomianism that have been made against him. [Acts 26:12–18] This account is briefer than the others. The speech here is again tailored for its audience, emphasizing what a Roman ruler would understand: the need to obey a heavenly vision,[Acts 26:19] and reassuring Agrippa that Christians were not a secret society.
God can chooses whom he wishes to in order to reveal something whether though visions or prophecies!
An interesting note to ponder would be about the pagan Sibyl prophecies that prophesied about many Christian events that were to eventually be revealed later.
In fact four of them are found on the ceiling of the Sistine Chapel in Rome.
The Sibyls were prophetic women who were resident at shrines or temples throughout the Classical World. The five depicted here are each said to have prophesied the birth of Christ. The Cumaean Sibyl, for example, is quoted by Virgil in his Fourth Eclogue as declaring that "a new progeny of Heaven" would bring about a return of the "Golden Age". This was interpreted as referring to Jesus.
In Christian doctrine, Christ came not just to the Jews but also to the Gentiles. It was understood that, prior to the Birth of Christ, God prepared the world for his coming. To this purpose, God used Jews and Gentiles alike. Jesus would not have been born in Bethlehem (where it had been prophesied that his birth would take place), except for the fact that the pagan Roman Emperor Augustus decreed that there should be a census. Likewise, when Jesus was born, the announcement of his birth was made to rich and to poor, to mighty and to humble, to Jew and to Gentile. The Three Wise Men (the "Magi" of the Bible) who sought out the infant King with precious gifts were pagan foreigners.
In the Roman Catholic Church, where there was an increasing interest in the remains of the city's pagan past, where scholars turned from reading Mediaeval ecclesiastical Latin texts to classical Latin and the philosophies of the Classical world were studied along with the writings of St Augustine, the presence, in the Sistine Chapel of five pagan prophets is not surprising.
It is not known why Michelangelo selected the five particular Sibyls that were depicted, given that, as with the Minor Prophets, there were ten or twelve possibilities. It is suggested by the Jesuit theologian John W. O'Malley that the choice was made for a wide geographic coverage, with the Sibyls coming from Africa, Asia, Greece and Ionia.
Vasari says of the Erythraean Sibyl "Many aspects of this figure are of exceptional loveliness: the expression of her face, her headdress and the arrangement of her draperies: and her arms, which are bared, are as beautiful as the rest."