What is the biblical basis for hearing God's audible voice today?
It seems that God spoke audibly at Jesus’ baptism in the Jordan by St. John the Baptist.
16As soon as Jesus was baptized, He went up out of the water. Suddenly the heavens were opened, and He saw the Spirit of God descending like a dove and resting on Him. 17And a voice from heaven said, “This is My beloved Son, in whom I am well pleased! - Matthew 3:17
God spoke to Moses on the Mountain of God according to the Book of Exodus.
3 One day, Moses was taking care of the sheep and goats of his father-in-law Jethro, the priest of Midian, and Moses decided to lead them across the desert to Sinai,[a] the holy mountain. 2 There an angel of the Lord appeared to him from a burning bush. Moses saw that the bush was on fire, but it was not burning up. 3 “This is strange!” he said to himself. “I’ll go over and see why the bush isn’t burning up.”
4 When the Lord saw Moses coming near the bush, he called him by name, and Moses answered, “Here I am.”
5 God replied, “Don’t come any closer. Take off your sandals—the ground where you are standing is holy. 6 I am the God who was worshiped by your ancestors Abraham, Isaac, and Jacob.”
Moses was afraid to look at God, and so he hid his face.
7 The Lord said:
I have seen how my people are suffering as slaves in Egypt, and I have heard them beg for my help because of the way they are being mistreated. I feel sorry for them, 8 and I have come down to rescue them from the Egyptians.
I will bring my people out of Egypt into a country where there is good land, rich with milk and honey. I will give them the land where the Canaanites, Hittites, Amorites, Perizzites, Hivites, and Jebusites now live. 9 My people have begged for my help, and I have seen how cruel the Egyptians are to them. 10 Now go to the king! I am sending you to lead my people out of his country.
11 But Moses said, “Who am I to go to the king and lead your people out of Egypt?”
12 God replied, “I will be with you. And you will know that I am the one who sent you, when you worship me on this mountain after you have led my people out of Egypt.”
13 Moses answered, “I will tell the people of Israel that the God their ancestors worshiped has sent me to them. But what should I say, if they ask me your name?”
14-15 God said to Moses:
I am the eternal God. So tell them that the Lord, whose name is “I Am,” has sent you. This is my name forever, and it is the name that people must use from now on. - Exodus 3:1-15
Let us also remember that Jesus spoke to St. Paul (Saul) in the Book of Acts.
9 Meanwhile, Saul was still breathing out murderous threats against the Lord’s disciples. He went to the high priest 2 and asked him for letters to the synagogues in Damascus, so that if he found any there who belonged to the Way, whether men or women, he might take them as prisoners to Jerusalem. 3 As he neared Damascus on his journey, suddenly a light from heaven flashed around him. 4 He fell to the ground and heard a voice say to him, “Saul, Saul, why do you persecute me?”
5 “Who are you, Lord?” Saul asked.
“I am Jesus, whom you are persecuting,” he replied. 6 “Now get up and go into the city, and you will be told what you must do.”
7 The men traveling with Saul stood there speechless; they heard the sound but did not see anyone. 8 Saul got up from the ground, but when he opened his eyes he could see nothing. So they led him by the hand into Damascus. 9 For three days he was blind, and did not eat or drink anything.
10 In Damascus there was a disciple named Ananias. The Lord called to him in a vision, “Ananias!”
“Yes, Lord,” he answered.
11 The Lord told him, “Go to the house of Judas on Straight Street and ask for a man from Tarsus named Saul, for he is praying. 12 In a vision he has seen a man named Ananias come and place his hands on him to restore his sight.”
13 “Lord,” Ananias answered, “I have heard many reports about this man and all the harm he has done to your holy people in Jerusalem. 14 And he has come here with authority from the chief priests to arrest all who call on your name.”
15 But the Lord said to Ananias, “Go! This man is my chosen instrument to proclaim my name to the Gentiles and their kings and to the people of Israel. 16 I will show him how much he must suffer for my name.”
17 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.” 18 Immediately, something like scales fell from Saul’s eyes, and he could see again. He got up and was baptized, 19 and after taking some food, he regained his strength. - Acts 9:1-19
If Christ can speak to Saul before his conversion, what would impede God from talking to someone audibly today. God is free to do as He sees right! The Holy Spirit can move as He wills and in very mysterious ways.
Just got a little side tracked with the following article about the phenomenon of some hearing the voice of Saint Clelia Barbieri.