Can a girl ask a guy out? because the guy is Extremely shy and he would never have the couage to ask her out?

Im 25, the guy is 28, We are both muslims ( mother european, father arab), we live in european country, our families know each other. His father likes me alot, i can see that, he sent me several times to go and talk with his son, but the son just answers my "Hi" then he escapes. his father told me his problem is that : "he is extremely shy" and he "doesnt have even the courage to even raise his head and look in the eyes" So the father gave up telling me in laughs "his son is not willing to get married and he wanna take him to the doctor cuz of that". His father told him to go with me to the cinema, he answered "yes, to the cinema, no problem" thats all. nothing else hapened. Its burning me from inside. Im going to their place this thursday. is it wrong if i take first step and ask him about the cinema? what should i say? in the presence of his father. not suitable for a girl to do so? the guy should show interest in the girl? im afraid to make a mistake, you know the islamic rules in man/woman relation. i dont want to look like cheap or in a hurry. But if i wait im 100% sure and afraid he would never ever make that magic golden first step, and i would die with grey hair waiting for him. Would appreciate any ideas.