The question is rarely phrased this way (largely because anyone who's read the Quran - Muslims especially - will tell you, Of course not. Allah emphatically denies it!). But people are again discussing the issue of whether Christians and Muslims worship the same God. So here are some thoughts I shared over at Between Two Worlds a few years ago on this post.
Do Christians and Muslims worship the same God? If you pay attention to what both religions are saying it turns out to be incredibly offensive to say Yes - given how insistent both religions are about their respective theological claims.
Here are some points in no particular order:
1) Let's let Allah define himself:
"He does not beget nor is he begotten." (Sura 112)
The Quran defines the god of Islam explicitly as not the God of the Bible. Let's respect Muslims enough to let them define who their god is. He is not the Father, Son and Holy Spirit. We honour their faith by speaking of Allah as another god - that is how Allah defines himself. From our perspective we cannot speak of Allah as anything other than an idol - anything else fails to take Muslim faith on its own terms.
2) Can anyone really imagine the prophets addressing the Edomites, Philistines etc saying 'Yahweh is very much like Baal/Molech/Asherah'? Never!
The question for the nations is not 'Do you believe in God?' But 'What god do you believe in?' Whether you're evangelizing in north Africa or north America "God" cannot be assumed. In fact "God" is the least obvious word in our evangelistic encounters. How on earth do we get to a position where people make it the point of commonality!
At this point a commenter replied that the 'Baal' analogies do not work because Allah is thought to be 'the transcendent Creator' and not simply a power within the world. He claimed that a Muslim convert would have to repent of many beliefs but not his belief in 'God as infinite transcendent Creator.'
To this I replied...
3) We don't say "Baal is called 'Lord' and receives worship therefore no convert from Baalism needs to repent of their notions of Lorship or worship." Of course they will have to repent of all of this. So then why would anyone claim that a belief in the 'infinite transcendent Creator' is of a different order? Fundamentally I see this as committing two errors. It is to say...
A) 'Transcendent Creator' is more foundational to God's being than His triunity.
B) The Muslim means roughly the same as the Christian when speaking of the 'Transcendent Creator'
I strongly disagree with both.
A) i) If God is transcendent Creator you've made Him dependent on creation.
A) ii) It is a position that leads to Arianism. Athanasius complained that Arius' error was to conceive of God as Unoriginate and then to consider trinity. On this trajectory he could never affirm the homo-ousios of One whose being was 'ek tes ousia tw patri' (out of the being of the Father). Similarly if your conversation with a Muslim begins with some 'bedrock' notion of transcendence before introducing them to Jesus it will necessarily mean introducing them to one who is less than the transcendent one. You'll have shot yourself in the foot from the very beginning. Let's not define Jesus out of full deity before we've even begun. We therefore must not begin on the Arian trajectory of affirming transcendent Creator first - Jesus will not come out very well from such a starting point!
B) Only the God who exists as Himself in relations of otherness can actually have a relationship with creation in which we can know Him as transcendent. 'Transcendent Creator' is dependent on trinity (not the other way around). The Muslim account of transcendence is completely confused (as is every unitarian account). Allah is a prisoner of his 'transcendence' - by definition cut off from any relationship with it (whether transcendent or immanent).
'Transcendent Creator' is neither the foundational nor a shared understanding of the living God. And it's not desirable that it should be.
At this point my interlocutor (rightly) suspected I was denying the possiblity of true philosophical reflection on divinity apart from Christian revelation. He claimed I was being overly Barthian. I replied with these points...
4) In terms of theological method, "Christ alone" is not a Barthian novelty! It's difficult to think of a more crucial verse in the history of the church for theological method than Matthew 11:27: "No-one knows the Father except the Son and those to whom the Son chooses to reveal Him."
To this let's add John 1:18; 14:6 and Colossians 1:15. To this let's add the continual Scriptural witness that we are blind, dead, enemies of God unable to know Him apart from His Word to us. (e.g. Ps 14:2; 2 Cor 4:4; Col 1:21). These plain and central truths cannot be evaded by crying 'Barthian'!
5) Nicea's "The Father Almighty, Maker of heaven and earth" was a deliberate and crucial choice of order. Triunity precedes creation. Of course it does - unless we want to define God as dependent upon creation.
6) Even Jews who have the Scriptures do not know the Father if they reject the Son. (cf ALL OF JOHN'S GOSPEL!)
7) To go over a previous point - there are tremendous Arian dangers of considering 'Creator' more foundational than trinity. Once you have assured your Muslim friend that she really does know God and that the God she knows is definitionally the infinite, transcendent Creator, do you really think you've helped her towards faith in Jesus of Nazareth? Have you not just given her every reason to reject divine honours (thus defined) being attributed to Christ. Won't she simply thank you for confirming her own doctrine of God which by definition precludes Jesus from being anything more than a prophet??
Athanasius rightly said 'the only system of thought into which Jesus Christ will fit is the one in which He is the starting point.'
The Rock upon which we build is nothing and no-one else but Christ. Let's be clearer on this whether we're evangelizing Muslims or our friends in the pub. They do not know God and besides - why would we want to confirm for them a sterile, non-relational doctrine of God in the first place? Let's tell them, 'The god you had thought existed was not God - let me tell you about the living God who is unlike anything you've imagined. His name is Jesus. Here is a God you can truly believe in!'