I can't see Steve Clarke choosing to go to Celtic, and if I'm honest I can't see Celtic approaching him. He's never had a European tie as a manager, and while I think that's a style of football that would be absolutely perfect for him, I think Celtic will go for someone with a proven track record of success in European competition.
The other option I can imagine them going for at Parkhead is David Wagner. A manager with inside knowledge of a top European club, but also with a proven track record of getting a club to punch above its weight - which is what's required at Celtic to get them out the rut they're in in Europe.
Like above posters, I don't see anyone coming in at this stage in the season. Lenny to come in, lose in the cup at Hibs, win the league, be relentlessly touted by Radio Scotland for months before the locks on the dressing room are suddenly changed around mid June.