The uncapped Spain international has been a first-team regular under the Northern Irishman, largely playing at full-back or at left wing.
Enrique has made a relatively muted start to the season, but Rodgers revealed the 27-year-old is currently playing through an injury.
“Jose has been playing with a little bit of an injury, but he’s still been showing his determination and pride for the team,” Rodgers told the Liverpool Echo.
“He has all the attributes to be one of the best left-backs in the Premier League.
“He’s a threat when he goes forward and defensively he’s very difficult to beat.
“The great thing is that Jose is always working at his game. He appraises himself honestly when we have chats. He’s one who is looking to improve his game and his passing.
“There’s no doubt that on his day he’s one of the best in that position in this country.”
Enrique has scored two goals in 70 Premier League appearances for Liverpool after completing a £7m move to Liverpool from Newcastle United in 2011.
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