Roque completed his €61m move to Barcelona in January but the 19-year-old has struggled for game time, seeing just 310 minutes over 13 appearances in all competitions.
Amid claims that Barcelona do not believe Roque is good enough to play for the team at this point, Mundo Deportivo report that a number of clubs have been in contact with the Brazilian's entourage over a possible loan move.
United are said to be keen to bring the 19-year-old to the Premier League, whole Napoli, Lyon, Nice, Sevilla and Real Betis are all credited with interest in Roque.
Barcelona manager Xavi has previously offered his support to Roque but recently left the door open to a loan move this summer.
"We have not decided anything yet," Xavi said. "We will decide at the end of the season what is best for everyone. It is not easy to arrive from Brazil. He needs time and adaptation. At the end of the season, we will decide."
According to SPORT, Roque has already ruled out the idea of leaving Barcelona on loan, with his agent prepared to complicate any efforts to part ways with the 19-year-old just six months after his move to Spain.
Roque's representatives believe he needs more time with Barcelona to get up to speed and hope Xavi decides to keep Roque around next season, although reports suggest the striker may not even end up getting registered in the squad next year because of financial concerns.
United are known to be on the hunt for a new striker and spent the January transfer window looking for an experienced goalscorer who could offer some support to young Rasmus Hojlund who, at the time, was struggling in front of goal.
However, a younger forward remains a possibility for United, who 90min understands are in the race to sign 20-year-old RB Leipzig striker Benjamin Sesko.