I think as long as a club not already in the Champions League, he'd stay here in the hope of getting into Europe (obviously only at Europa level) so if none of the top 4 in England, Spain, Italy or Germany were to bid, he might stay. I dont know about the top 4 in the foreign leagues, but from England we can only expect Arsenal to be possibly looking at LBs IMO (out of the top 4), and Bayern Munich also appear to be looking. Madrid have Marcelo, but it wouldnt be crazy to see them bid for Enrique. Same for Barca, who's LBs are all around 30 and declining in quality. Realistically I dont see him going to either, at least not right now before he's more established. Looking at other clubs who have been linked with him, Man U have Evra on a long deal, and supposed interest in Izzaguirre, while AC Milan signed Taiwo on a free. Also if you think about it, Clichy's move to Liverpool doesnt appear to have much substance to it, so Arsenal might not even need Enrique.
I know this is long, but I'm going somewhere, trust me. Based on my theory that he'd only leave for CL football, I think only Arsenal or Bayern would be likely to bid this summer (I did miss a few 3rd/4th placed teams in the foreign leagues, anyone clued up know if they're in the market for LBs?).
Not sure how much sense that makes but basically I dont think there's loads of clubs who'd want him, that he'd leave us for. 2 at my estimate.