According to German newspaper Bild, Bayern have been tracking the Spanish full-back over the last few months and are said to have offered in excess of £9million.
But Enrique has been heavily linked with a move to Liverpool, and it is believed a 'nod-nod wink-wink' deal with Liverpool is already in place.
Liverpool manager Kenny Dalglish is a big admirer of the former Vilarreal defender and, with Paul Koncheskey and Emiliano Insua both expected to leave at the end of the season, Dalglish is said to have the deal stitched up.
Enrique has refused to begin discussions about a new contract and has admitted that he wants to play European football next season.
All we can get from Enrique is: "It is flattering that Liverpool are interested."
Liverpool are currently in fifth place and will battle it out with Tottenham to try and secure a place in the Europa League,