After Wes Morgan, Christian Fuchs, and Eldin Jakupovic signed one-year deals last week, deep-lying midfielder Mendy is the only senior player in the City squad whose current contract expires this summer.
“He's extended through to the end of this season, which is great," Rodgers said. “Papy is one who we would like to keep. He's one of those players who's got a role to play.
“The longer I've been here, the more I've seen him and the more impressed I've been with him.
“It's been very clear that Wilf has been outstanding in the role he has played, but going forward I can see definitely a role for him here so we would want to keep a hold of him, especially if we can get European football, because the games will come thick and fast, so to have someone of his experience, quality and maturity around will be very important.
“I can't speak highly enough of him. He obviously hasn't played anywhere near as much as what he'd done before but every single day he's first class and as a manager and coach, you want that type of player around.
“He understands his role, he respects how well the team has done, but every time he's come in, he's played a very important part.
“I know the club is in talks with his representatives, and he's definitely one I'd like to keep."
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