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Keita, 27, joined the Reds in a £52.75m move from RB Leipzig in 2018 but has largely failed to live up to expectations since arriving at Anfield.
The Guinea international has managed only 11 goals in 116 appearances for Liverpool, with his four seasons at the club hampered by persistent injury problems.
However, Guinea-based outlet Imedias.net claims PSG are considering a move for the midfielder, who has one year remaining on his current contract with Liverpool.
According to the report, PSG are prepared to pay up to €50m (£42.5m) for Keita.
It is also claimed that Luis Campos, who is expected to replace Leonardo as sporting director at the Parc des Princes, is a fan of the midfielder.
Campos is said to see Keita as the ideal replacement for Georginio Wijnaldum, who has struggled since joining PSG on a free transfer from Liverpool last summer.
PSG announced their first signing of the summer on Tuesday, with Nuno Mendes joining in a £34m move from Sporting Lisbon after a successful season-long loan spell at the Parc des Princes.
The deal follows reports that striker Kylian Mbappe has been given control of the 'sporting project' at PSG after signing a new three-year deal at the club.
Reports in Spain claim that Mbappe was promised a say over transfers and would even have the power to change coaches, if he committed his future to the club.
Mbappe turned down a move to Real Madrid earlier this month to sign a new three-year deal at the Parc des Princes, becoming the highest-paid player in world football with wages of around £1m a week.
Yep I’d take that— Liam Moore🔴 (@LiamMooreLFC) May 31, 2022
I'd take it, love him but he's just to inconsistent and if we want to be challenging City each year we need a better number 8.— Archibald The Great (@Archibald1010) May 31, 2022
I'd personally drive him there for 50m lmao— Borislav P. (@Abdaling) May 31, 2022
Would be crazy not to accept that offer. Take the money and but a midfielder up to the LFC level. Naby just hasn't been able to settle. This would be great for all involved.— Gamerdad (@gamerdad1981) May 31, 2022
Liverpool fans on social media are split over whether the club should sell Keita this summer.
"No f*****g chance we can't lose another midfielder," wrote one Twitter user.
But another posted: "I'd take it, love him but he's just too inconsistent and if we want to be challenging [Manchester] City each year we need a better number 8."
Should Liverpool sell Keita this summer? Let us know your thoughts.