I think Rogers said he's staying at Celtic (although these days, that's always no guarantee it'll happen) but I can't imagine fans of either of those clubs being overwhelmed at him being appointed. Don't think Arsenal's board will look at him, Chelsea probably more likely but I can see someone like Allegri being more their choice.
I'm sure he'd leave in a flash if a club like Arsenal or Chelsea wanted him, but I doubt that he'd be anywhere near the top of their lists.
As for Stevie G vs Rodgers. I guess I'll have to be cheering Stevie on
I can't stand Celtic anyway, not that I am a fan of Rangers or anything, and admittedly I am not going to see any of the games, being as they aren't on tv here anyway! But I do wish him well, from what I read, it's a really tough job for him, but at least he seems to have assembled a good team with him there, so hopefully it'll go far better than many seem to be expecting.