The 22-year-old has been a regular for the Red Devils during the 2023-24 campaign, making 13 appearances in all competitions, but is yet to score and has only contributed one assist.
Pellistri made the move to Old Trafford from Penarol in 2020, and he has featured on 23 occasions for the club, with 13 of those outings coming in the Premier League, but he is still waiting for his first goal.
The Uruguay international only has a contract with Man United until June 2025, and there has recently been a host of speculation surrounding his future with the club.
A number of teams are thought to be keen to sign him on loan this month, but according to The Sun, Villarreal want to bring him in on a permanent basis before the end of the January transfer window.
The report claims that fit-again Amad Diallo is ahead of Pellistri in the thinking of Man United head coach Erik ten Hag, so the Uruguayan could struggle for action in the second half of this season.
The Red Devils are said to be willing to listen to offers for the forward, although it is still possible that he could depart on loan in January rather than permanently.
Pellistri was a late substitute against West Ham United in the Premier League on December 23, but he has not featured in the team's last two league games with Aston Villa and Nottingham Forest.
The South American has experience of operating in La Liga, having had two separate loan spells at Alaves during the 2020-21 and 2021-22 campaigns.
Pellistri played 35 times for Alaves over the two seasons, but he did not contribute a goal or an assist.
Donny van de Beek's exit from Old Trafford has already been confirmed, with the Netherlands international moving on loan to Eintracht Frankfurt for the second half of the campaign.
Meanwhile, Jadon Sancho is on the verge of returning to Borussia Dortmund on loan, with a deal expected to be confirmed by the end of the weekend.
Hannibal Mejbri and Dan Gore also being linked with short-term departures, and there could potentially be one incoming this month, with a new striker said to be a priority for head coach Ten Hag.