There are many possibilities that your brother-in-law himself doesn’t even know why he is doing that and being clingy is not necessarily have to do anything about to do with his sexuality. Do observe him more and then confront him. It’s possible that he likes you as a person and is very comfortable with you. Try to talk to your brother-in-law first and come to a conclusion about his sexuality. If he says he is confused then ask him to try some sexuality questionnaires which might help in finding out his sexuality.
Talking about sexuality is a very personal and sensible thing to discuss, therefore you shouldn’t involve your wife in this matter. Also, make sure not to offend your brother-in-law in any way possible while discussing this. It would be great if you can reassure him that even if he is gay it won’t change anything between you both.
The above ideas are suggested only if your brother-in-law doesn’t know about his sexuality but if he says that he is gay then talk to him about his behavior and ask him to stop doing them with you. But here also you have no right to talk about his sexuality to your wife. It’s a very personal thing and he should decide when to come out of his closet.