The Reds legend sees his current deal expire at the end of the season and could therefore leave after eight glittering years at Anfield.
After he scored two goals in Liverpool's 3-2 win at Southampton on Sunday, Salah said he's not received any offers from the club to stay.
He also claimed he's 'probably more out than in', and his comments have not sat well with fellow club legend Carragher, who called him 'selfish'.
Speaking on Monday Night Football for Sky Sports on Monday, he said: "Of course there's been discussions.
"Right now, there's obviously a big difference in the valuation, what Mo Salah and his agent value themselves at, whether that's financially or in terms in length of contract, to what Liverpool do.
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"So the reason Liverpool wouldn't have offered a contract yet is because Mo Salah will turn it down. So they're still in talks, maybe... I'm desperate for them to meet in the middle. But I must say, I am very disappointed with Mo Salah."
Presenter David Jones asked why, with Carragher then replying: "That interview yesterday, last night after the game and it comes out today.
"Liverpool have got Real Madrid midweek and they've got Manchester City at the weekend, that's the story for Liverpool right now.
"Mo Salah, we're all quite aware, certainly the local reporters are in Liverpool, that in the seven years he's been at the football club, he's stopped in the mixed zone twice, which is his right, which is absolutely fine.
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"But he decided to stop for the third time away at Southampton on the back of winning Liverpool the game and putting that out.
"Now, the most important thing for Liverpool Football Club this season is not the future of Mo Salah, it's not the future of Virgil van Dijk and it's not the future of Trent Alexander-Arnold.
"The most important thing is Liverpool winning the Premier League, that is more important than any of those players.
"And if he continues to put comments out or his agent keeps putting cryptic tweets out, that's selfish, that's thinking about themselves and not the football club."
Jones then asked if perhaps that Salah does not feel as though he is getting the love he deserves at Liverpool.
However, Carragher responded: "Well, he's certainly getting the love from me and Liverpool supporters and they're in talks, that is part of football.
"I would say Mo Salah is in the top five players to ever play for Liverpool Football Club. I would go Steven Gerrard, Kenny Dalglish, Graeme Souness, Ian Rush, and I'd put Mo Salah in fifth position. That's how highly I rate him, that's how special this guy is..."
"So give him what he wants, surely?" asked Jones, but Carragher said: "No. It's not about giving somebody what they want.
"But, what I would say is, I hope Mo Salah and the other two players who are involved in this, Virgil van Dijk and Trent Alexander-Arnold, [don't] feel like this club will fall apart if they ever move on.
"Steven Gerrard left the football club, the next manager came in and won the league. Steven Gerrard didn't win the league, Jurgen Klopp won the league with a new team.
"Kenny Dalglish, at that time Liverpool's greatest ever player, when he stopped playing, Peter Beardsley came in and was part of probably the greatest footballing team we've ever seen in a red shirt in 1988.
"Graeme Souness left, Liverpool won the double for the first time in their history two years later in 1986. Ian Rush moved on, after him came John Aldridge, and then later when Ian Rush moved on, Robbie Fowler came.
"And Salah, would we miss him if he moved on? Of course we would but I can assure you, Liverpool will move on."
Salah has scored 223 goals in 367 appearances for Liverpool across all competitions, with the Egyptian assisting another 99.
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The 32-year-old is the club's record goalscorer in the Premier League with 165 goals, which puts him eighth in the league's all-time list.
He has been pivotal to Liverpool's success in recent years that has included Premier League and Champions League triumphs.
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However, this could be Salah's final season at the club, especially if he and the club are unable to agree on a new contract.
talkSPORT reported earlier in the month that Saudi Arabian club Al Hilal want to sign the winger ahead of the Club World Cup.