The Uruguay international made the move to Old Trafford from Penarol in October 2020, but he has only featured on 10 occasions for the Red Devils during that time.
All of his appearances for the English giants came last season, including four in the Premier League, but there has been widespread speculation surrounding his future this summer.
Pellistri is currently with the Man United squad in the United States, and he was a second-half substitute in the team's last match against Real Madrid on Wednesday night.
The 21-year-old also featured against Arsenal last weekend and said following the clash with the Gunners that he had held talks with Red Devils head coach Erik ten Hag over a summer exit.
"Yes, I have spoken to him (Ten Hag) and we are working together to find the best club, the best way, the best option. I am happy with that way because we are all in the same position," he told reporters at the time.
"[I'm hoping] to play. In my position and at my age, what you want is to play. We are looking forward to find the best solution to do that. I felt amazing whenever I played for Manchester United. I want more of that."
According to journalist Luis Fregossi, Boca are currently keen on the South American, with the Argentine giants looking to discuss a loan move with the Red Devils.
Pellistri has had two separate loan spells away from Man United during his time at the club, representing Alaves during the 2020-21 and 2021-22 campaigns.
The forward is still thought to be in Ten Hag's long-term plans, and he has another two years left to run on his contract at the club, with the option of a further 12 months.
However, Pellistri is down the pecking order when it comes to the starting roles in the wide areas, and Amad Diallo's impressive form on loan at Sunderland last term has seemingly put the Ivory Coast international firmly in Ten Hag's plans for the new campaign.
Pellistri will hope to be involved in Man United's final friendly of their pre-season tour of the United States against Borussia Dortmund on Sunday evening.
The Red Devils will then head back to Europe for their last two pre-season matches of the summer against Lens and Athletic Bilbao, before beginning their 2023-24 Premier League campaign at home to Wolverhampton Wanderers on August 14.