The Uruguay international is currently being heavily linked with a loan move away from Old Trafford, and it had been thought that Granada were closing in on his signature.
Pellistri has experience of La Liga football, having represented Alaves on 35 occasions during two separate loan spells, with 33 of those outings coming in Spain's top flight.
Granada had Alvaro Fernandez on loan from Man United until earlier this month, with the Spaniard leaving the club in order to move to Benfica on an initial loan deal, which could become permanent this summer.
Last week, it was claimed that 'advanced discussions' were taking place over Pellistri, with Granada appearing to be winning the race to secure his signature.
However, according to the Daily Mail, while Pellistri is keen to move to the Spanish club, Man United are not prepared to accept what they deem to be 'a token contribution to his salary'.
There is allegedly a chance that a deal could be revived, if Granada are prepared to change the terms of their previous offer, but other clubs are also showing an interest.
The 22-year-old has been a regular in Man United's first-team squad this season, and he has featured on 14 occasions in all competitions, with nine of those outings coming in the Premier League.
Pellistri is yet to score and has only managed one assist in 2023-24, though, and the return of Amad Diallo from injury has pushed him down the pecking order.
The South American made the move to Man United from Penarol in 2020, and he has represented the 20-time English champions on 24 occasions, failing to score and only managing two assists.
Despite his struggles at club level, Pellistri is very much a part of the Uruguay set-up, featuring on 18 occasions, and he represented his country at the 2022 World Cup.
PSV Eindhoven and Villarreal are among the clubs to be linked with his services this month, although it is unclear at this stage whether either team are preparing to make an offer.
A recent report also claimed that Man United had failed with a swap deal involving Pellistri and Sporting Lisbon's Morten Hjulmand.
Pellistri was back in training at Carrington on Tuesday morning, with the players returning from their winter break, and the Red Devils are currently preparing for Sunday's FA Cup fourth-round contest against League Two outfit Newport County.