Is it possible to even witness to a Muslim? Is there any way to reach them? Yes, there is a way to witness to Muslims.
All Have Sinned
To be sure, Muslims are no different than any other person who doesn’t know Christ; they are sinners. All of us have fallen infinitely short of God’s glory (Rom 3:23), and not one of us can say we’re a good person or that we do good (Rom 3:10-11). It’s no different witnessing to a lost family member than it is to a Muslim because they all (we all) have sinned and need a Savior. They might know about Jesus but the question is, “Does Jesus know them?” It’s not what we know but Who we know, and if we know Christ, then Christ knows us. Otherwise, listen to what He says: “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven” (Matt 7:21), for ”On that day many will say to me, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?’ And then will I declare to them, ‘I never knew you; depart from me, you workers of lawlessness” (Matt 7:22-23). Yes, many claim to know Him but the question above all is, “Does Jesus know you?” We might claim to have done “many mighty works in [His] name,” but that is worthless without the righteousness of Christ because works done outside of Christ are nothing more than filthy rags to God, and He will not accept them (Isaiah 64:6).
Good People Don’t Exist
When I was witnessing to a Muslim I asked him if he thought he was a good person and he said yes, so I told him that even Jesus said only God was good (Mark 10:18). No human can classify themselves as good because God hasn’t. We are made acceptable to God only through trusting in Christ. There is no other way possible (Acts 4:12). The good news is that most Muslims I know are open to talking about spiritual things. In the Koran, Jesus is presented as the One who did great miracles, including raising the dead (Sura 19:25), but He is also presented as sinless (Sura 19:19), and as born of a virgin, so you’ve already got a good starting point in a conversation. They might even like the fact that you know something about their book, but Muslims at least will acknowledge that Jesus has ascended to heaven, so you could say, “Since Jesus went to heaven, we know He knows the way, so do you want to know the way to heaven too?” Obviously they want to know, but most Muslims I’ve spoken with or communicated with are never quite sure they’ve done enough to go to heaven. They might have a good idea, but the vast majority can never be sure, but the good news is, we can tell them how they can be sure.
The Bible says that “The king’s heart is a stream of water in the hand of the Lord; he turns it wherever he will,” (Prov 21:1), so God can change the human heart, even if it’s a pagan king, so the same thing applies to Muslims. God changed Saul’s heart and so He had to change his name (Paul), and remember Saul was a persecutor of the church. He was condoning the stoning of believers, and who among the first century Christians would have ever tried to go up to Saul and witness to him? There is no record of anyone ever trying to share Christ with him. It would take a supernatural intervention for Saul to become Paul, and that’s just what happened (Acts 9), so God can change any heart He wills to, even if it’s an arch-enemy of the church and hates Christians. God’s Spirit can change a person so much that it’s like they have a new heart. Ezekiel wrote about such a change when he wrote down that God said, “I will give you a new heart, and a new spirit I will put within you. And I will remove the heart of stone from your flesh and give you a heart of flesh” (Ezk 36:26).
Dreams and Visions
I have heard of many Muslims having dreams about Jesus, so God may have to use dreams to reach Muslims because of the limited number of Christians in Muslim countries and there is scarcely a Bible to be found, but God can move heaven and earth to reach one soul. He has and He still is. Nothing is too hard for God, so what might seem impossible for us, is not for God (Luke 1:37). Paul spoke with a group who believed in mythological gods by saying, “The God who made the world and everything in it, being Lord of heaven and earth, does not live in temples made by man, nor is he served by human hands, as though he needed anything, since he himself gives to all mankind life and breath and everything” (Acts 17:24-45), and God has opened the way for all nations to come to Him, which may explain why Paul said that God “made from one man every nation of mankind to live on all the face of the earth, having determined allotted periods and the boundaries of their dwelling place, that they should seek God, and perhaps feel their way toward him and find him. Yet he is actually not far from each one of us” (Acts 17:26-27). God does not respect one nation over another, just as He doesn’t regard Gentile over Jew. There is no race to God…but there is only grace, and it’s open to all who will believe. And even if they’re sworn enemies of Christ, we are to pray for our enemies (Luke 6:27).
We must always be ready to give an answer for the hope that is within us, but as Peter said, do “it with gentleness and respect” (1 Pet 3:15c). No one was ever debated into the kingdom or argued out of what they believe. It must be by a quiet, gentle spirit that we show them Christ. We must allow God to do the converting as only He can do. We can only do more harm than good by trying to convert someone, so use the Word of God and the Spirit of God and pray that they would become a child of God. We can point them to Christ, but it must be God’s Spirit that reveals Who Christ is. Agnostics, atheists, Muslims, Buddhists, or whoever, God alone can change their heart by His Spirit, but we must at least try to witness to them but then leave the rest up to God. God uses us as fishers of men but God is the Lord of the Harvest. We are not.
Here is some related reading for you: Why Christians Must Love Muslims 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), Crossway Bibles. (2007). ESV: Study Bible : English standard version. Wheaton, Ill: Crossway Bibles. Used by permission. All rights reserved.