Discussions with Milner’s representatives are yet to take place, however, indicating that reports on Tuesday the club have made him an offer are wide of the mark.
Milner’s current deal expires in the summer and the manager wants to have the 36-year-old in his squad next season.
The ex-England international has continued to play an important role in Klopp’s squad this season despite his advancing years, making 16 Premier League appearances and four in the Champions League.
It is understood Klopp is keen for the midfielder to extend his stay for at least another season.
“There is no chance Milly will retire next year, he is desperate to play on and I understand,” he said on Friday.
“Life after your career, when you are lucky enough to stay healthy, is much longer than your career so you usually extend your career as long as you can if you can play football.
“I think Milly will be fine after his career as well but he obviously loves what he is doing and he will play football next year, definitely.”