Despite criticising Rodgers in a newspaper interview, claiming he and the club reneged on a deal to allow him to leave for a Champions League club, the Reds boss does not feel the striker has a debt to repay to Liverpool and their fans.
"This club has given every single player here everything in the time I've been here and none more so than Luis," said the Northern Irishman.
"He will show that and demonstrate that in his performances and that is what the players and people want to see.
"They want to see him with a red shirt on fighting for the club.
"The great thing about this football club is no matter what a player has done - or supposedly said - the supporters are 150 per cent behind every player that pulls on that shirt and they back them to the hilt.
"I am sure that is something we will see and aligned to that will be his commitment, and that will be nothing more than I would expect.
"I have no doubt, having been out, he will be even hungrier but his commitment and fight for the cause will still be the same."