Liverpool's owners Fenway Sports Group are keen to tie manager Jurgen Klopp down to a new, long-term contract.
The German has just delivered the club's sixth European Cup, their first major trophy for seven years, and guided them to a second-place finish in the Premier League with a record runners-up points tally of 97.
Klopp's current deal expires in 2022 but FSG, essentially principal owner John W Henry, chairman Tom Werner and FSG president Mike Gordon, want to secure him for longer.
"When the players threw Jurgen in the air last night after our victory, they were acknowledging what all Liverpool fans know- he is beloved by all who appreciate football," said Werner.
"Jurgen is a brilliant coach but just as importantly, he is a humble and caring man who is happy today because he knows what yesterday meant to our supporters."
For his part, Klopp was amazed by the 500,000-plus turn-out for the team's victory parade in the city on Sunday.
"I don't know exactly how many people live in Liverpool but it does not look like there is a lot of space for fans of other clubs," he told LFC TV.
"It is incredible. If you are a young kid, which do you support?
"There are not a lot of opportunities or options other than Liverpool. You see in the eyes how much it means. It is really intense."
Klopp most important figure at Liverpool - Carragher
Jamie Carragher, the Sky Sports pundit and former Liverpool centre-back, said after the Madrid final that "special" Klopp was the most vital figure at the club and urged the owners to hand him an extended deal.
He said: "I think [Klopp] is the number one at the club. He's the manager of course, but what I mean is he is the most important figure. If you asked me would I rather lose Virgil van Dijk or the manager, I'd say Van Dijk. I think he is a special manager.
"I don't know what his contract situation is but give him a new one and hopefully now, he can push on. He's got that monkey off his back with that first big trophy, first time he's won the Champions League after so many finals without a win.
"Hopefully for him and that set of players, it's not just a one-off. He's always done seven years at his clubs so in 2022 [when Klopp's current contract runs out], it will have been seven years. Let's try and make it 17!
"The next step is to continually compete, as they have done this season, for the Premier League and Champions League. The Premier League is the big one Liverpool want of course, but Man City are such a good side, it's going to be difficult.
"At this moment, Liverpool are well equipped. They've won the Champions League so they're going to be there or thereabouts for most seasons in the competition now and they have to do that in the Premier League, which is something we (the teams Carragher was in) never did enough of. That's what they have to do next season is really push Man City."
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