The Egyptian's contract with the Reds is set to expire next summer, with the 32-year-old able to negotiate with international clubs starting in January for a potential free transfer in the following year.
Salah has been a long-term target of the Saudi Pro League, while recent reports have suggested that European duo Paris Saint-Germain and Real Madrid also retain an interest in the Reds star.
Paris Saint-Germain step up chase for Liverpool star Mohamed Salah
Salah has made an excellent start to the season with Liverpool, netting six goals and providing five assists in nine games so far, as transition from the Jurgen Klopp era to new boss Arne Slot has gone smoothly so far.
With Salah continuing to find the net regularly in both the Premier League and Champions League, French champions PSG are reportedly ready to step up their bid to sign Salah next summer.
According to The Sun, PSG believe that Salah can play for another three years at the highest level and want to bring him in as their latest marquee signing following the exits of Lionel Messi, Neymar and Kylian Mbappe over the past few summers.
Many believed that a move to the Saudi Pro League, where Salah could become the face of the sport, was growing increasingly inevitable, but the report claims that the player does not want to move there at this stage of his career and would prefer to stay in Europe.
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PSG are one of the only clubs that would be able to get close to the huge salary that Salah could earn in Saudi Arabia and the club's owners are said to be wanting to rebuild the squad in the wake of Tuesday night's 2-0 defeat to Arsenal in the Champions League.
Salah said last month that he had not spoken to anyone at Liverpool about a new deal. “Nobody in the club has talked to me about contracts. It is not up to me, it is up to the club," he said.
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“As you know, it’s my last year in the club. I just want to enjoy it, I don’t want to think about it. I feel I’m free to play football and let’s see what’s going to happen next year.”
Liverpool would not be able to match any wage offer that PSG and the Saudi Pro League would be able to tempt Salah with and in FourFourTwo's view, the club will have to rely on their existing relationship with the player, who is valued at €55 million by Transfermarkt, and the role he can play in Slot's new regime if they are to convince him to stay at Anfield beyond this season.