Catholic officially said that Muslim God and Catholic God is same.
Lumengentium II/16
16. Finally, those who have not yet received the Gospel are related in various ways to the people of God.(18*) In the first place we must recall the people to whom the testament and the promises were given and from whom Christ was born according to the flesh.(125) On account of their fathers this people remains most dear to God, for God does not repent of the gifts He makes nor of the calls He issues.(126) But the plan of salvation also includes those who acknowledge the Creator. In the first place amongst these there are the Muslims, who, professing to hold the faith of Abraham, along with us adore the one and merciful God, who on the last day will judge mankind. Nor is God far distant from those who in shadows and images seek the unknown God, for it is He who gives to all men life and breath and all things,(127) and as Saviour wills that all men be saved.