The Italy international is surplus to requirements at PSG this season, with the club's new head coach Luis Enrique leaving the 30-year-old out of his first two Ligue 1 squads.
Al-Ahli are thought to have already agreed personal terms with the central midfielder, but the Saudi Pro League outfit are yet to find an agreement with PSG in terms of a transfer fee.
According to L'Equipe, Man United are keeping a close eye on the situation, and the 20-time English champions 'cannot be ruled out' when it comes to potential suitors for him.
The report claims that Bayern Munich are also contenders for his signature, with the Bundesliga giants bidding to improve their midfield options before the end of the summer transfer window.
Verratti made the move to PSG from Pescara in the summer of 2012, and he has represented the capital giants on 416 occasions, scoring 11 goals and registering 61 assists in the process.
The Italian featured 38 times at club level during the 2022-23 campaign, including 29 appearances in Ligue 1, but it appears that he has played his final match for the Paris side.
Verratti has won nine league titles during his time at PSG, but he has been unable to help the club secure Champions League glory, coming closest in 2019-20, when the French team lost to Bayern in the final.
Man United have already boosted their midfield department this summer with the signing of Mason Mount, but Fred has left the club, while Scott McTominay and Donny van de Beek are being linked with departures.
Fiorentina's Sofyan Amrabat has long been regarded as Man United's leading target in the middle of the park, but the club are yet to submit an offer for the Morocco international.
Liverpool have also reportedly held talks with the midfielder's representatives to discuss a potential move to the Premier League before the end of the transfer window.
Amrabat was an unused substitute in Fiorentina's Serie A opener against Genoa on Saturday in a clear indication that he will be leaving before the market closes.
Man United again struggled in midfield against Tottenham Hotspur in the Premier League on Saturday, with Casemiro often left isolated when Bruno Fernandes and Mount broke forward.
As well as a midfielder, the Red Devils are thought to be considering the forward options available amid claims that Anthony Martial could depart before the window closes.