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The report comes after PSG head coach Christophe Galtier said at a press conference on Thursday that he wants to sign a new striker this summer, with Mauro Icardi and Arnaud Kalimuendo expected to leave the Parc des Princes.
"We will sign a new striker, as we're looking to find a solution for Mauro Icardi and also Kalimuendo will join Rennes," said Galtier, as reported by Fabrizio Romano.
Rashford, 24, has one year remaining on his current deal with boyhood club Manchester United, who hold an option to extend his contract by a further year.
The England star struggled for form and fitness last season, managing just five goals in 32 appearances in all competitions.
He started United's opening game of the new season against Brighton on Sunday but was unable to find the net as the Red Devils were beaten 2-1 at Old Trafford.
PSG manager Galtier: “We will sign a new striker, as we’re looking to find a solution for Mauro Icardi and also Kalimuendo will join Rennes”. 🚨🔴🔵 #PSG— Fabrizio Romano (@FabrizioRomano) August 11, 2022
“We respect Keylor Navas, he does not want to be 2nd goalkeeper - it’s normal. I’m told there are clubs now interested”. pic.twitter.com/YXR1PqoBF0
French journalist Julien Laurens claims Rashford is "keen" for a new challenge but says no discussions have taken place between PSG and Manchester United over a deal for the striker.
"Confirmation of the contacts between PSG and Marcus Rashford, as reported first by L'Equipe," tweeted Laurens.
"PSG need a player who can play wide or as a 9. Rashford is keen on a new challenge, one year before the end of his contract.
"No discussions yet with Manchester United."
PSG could struggle to convince United to sell Rashford, who has scored 93 goals in 303 games for the club since making his senior debut back in 2016.
Confirmation of the contacts between PSG and Marcus Rashford, as reported first by L’Equipe. PSG need a player who can play wide or as a 9. Rashford is keen on a new challenge, one year before the end of his contract. No discussions yet with Manchester United. @ESPNFC— Julien Laurens (@LaurensJulien) August 11, 2022
United are already in the market for reinforcements up front, as the uncertainty surrounding Cristiano Ronaldo's future continues.
The Red Devils were in talks to sign veteran striker Marko Arnautovic from Bologna but pulled out of negotiations after having a £7.2m bid rejected by the Italian club.
United manager Erik ten Hag would be left with severely limited options in attack if Rashford was allowed to join PSG.
Anthony Martial is currently sidelined with a hamstring injury, while Mason Greenwood remains suspended - leaving only Ronaldo, who himself handed in a transfer request earlier this summer, as the only other senior striker in the squad.