The Belgium international did not start a game for the Reds last term, but Klopp has said he wanted the former Sunderland keeper to stay on Merseyside.
According to the club's official website, Klopp hailed the 31-year-old's professionalism and said he is "grateful for everything Simon has done for me."
"If you were to ask me to write a list of the most standout professionals I’ve worked with in the game—in a career of well over 30 years—Simon Mignolet would be competing for the number one spot.
"The respect he commands in our dressing room is unrivalled. An outstanding athlete, an outstanding person, and an international-class 'keeper.
"The truth is I don't want Simon to leave—why would I? He's a 'keeper good enough to start for all the teams in the Premier League.
"But this is a little like the situation we faced with Lucas Leiva a few seasons ago now. Sometimes you have someone whose contribution to the club means you have to consider their welfare also. Simon is such a person."
Mignolet joined Liverpool in 2013 after three impressive seasons with the Black Cats. The Belgian had developed into one of most promising stoppers in England, and former Reds coach Brendan Rodgers made him his No. 1.
The 'keeper's career at Anfield wasn't plain sailing, and the arrival of Loris Karius in 2016 under Klopp saw Mignolet drop to the bench. However, the player recovered the German's confidence and reclaimed a starting berth midway through the season.
The signing of Brazil international Alisson Becker from Roma for a world-record fee for a goalkeeper 12 months ago all but ended Mignolet's starting chances with the reigning UEFA Champions League holders.