Jurgen Klopp is hoping Mo Salah, Virgil van Dijk and Trent Alexander-Arnold all pen new contracts at Liverpool.
The former Reds boss was speaking at the unveiling of his new role - global head of soccer at Red Bull - when he was asked about his former players. All three are out of contract this summer and have yet to agree new deals.
He said: "He (Salah) is the biggest striker Liverpool had in modern times. Fantastic player, fantastic human being, outstanding athlete, best ambassador (Egypt) could have. Fantastic really in very much all departments. So I hope he will stay at Liverpool.
"From my point of view I would love all three of them to extend their contracts, but I don't know. They didn't tell me."
Klopp joked when asked about the possibility of the trio joining Red Bull's network of clubs in the future, in which he referenced criticism of right-back Alexander-Arnold's defending.
The German said: "Oh, yeah - Virgil, I'm pretty sure he would love to have now five more years at Liverpool and then between 41 and 44 for New York Red Bulls because he probably underestimates US football. But open arms, no problem.
"Mo, yes, would love to - I don't think we have a chance to pay him to be honest.
"And then Trent, yeah, and he could finally learn defending, eh? I can't believe that you all discuss this still, it's so poor and I'm really happy I'm not part of that.
"I watched the press conference when he (Klopp's successor Arne Slot) had to talk about it, and you think 'oh my God, they still don't understand it'!
"And yes he didn't play well against Manchester United (the 2-2 draw at Anfield on January 5), but if you would make such a fuss of him when he plays well, like you make a fuss of it when he doesn't play well, that would be really a cool planet."
Klopp is in touch with his former players and is enjoying watching Arne Slot’s side, who sit top of the Premier League and Champions League tables.
He has no regrets about leaving Anfield but he joked he might return for a party should Manchester City be stripped of any league titles following the result of their hearing into 115 charges around financial rule breaches.
The German added: “Whatever we have to celebrate, we would do it, good weather, stuff like this, we would have our own parade in my garden. We will see. I didn't follow it at all. Let's see."