a) take a deep breath, this is definitely not something to go overboard with.
As much as it sucks right now, in time whatever this thing is, it WILL blow over.
b) just talk to him....explain that whatever this rumour is is just indeed a rumour.
But by the sounds of it there is something you need to apologize about??
So....apologize.
I can't guarantee everything'll work out--depending on what happened, some people are not as forgiving, and some things are not easy to forgive, so I can't tell you exactly what's going to happen.
But my advice is talk to this guy, explain everything and sort everything out.
That's honestly the only advice I can give you, there's nothing else really for you to do.