The title winner will leave the Foxes as his contract expires.
Rodgers said, "Danny is an interesting one because there's a perception about how he works, but I have to say, he is absolutely first-class.
“He just wants to play now. He's a good player, a good guy, I have enjoyed working with him. He trains like a demon every day.
“He's at the age where he is still fit and he doesn't want to be a back-up player. He still has a few years at this level to be a starter somewhere and that's why he will move on.
"Unfortunately, he hasn't been able to play because of Ricardo (Pereira), but I'm sure he will get a great club and go on to show his talent."