The Red Devils kicked off their summer spending last weekend by bringing in Joshua Zirkzee from Bologna, with the Netherlands international boosting the club's forward options.
On Thursday, the club then announced the capture of Leny Yoro, with the 18-year-old arriving at Old Trafford in a high-profile move from Lille.
The club are also in talks with PSG over a move for Manuel Ugarte, having seemingly identified the Uruguay international as their leading midfield target this summer.
However, according to L'Equipe, Man United are also huge admirers of Simons and could make an attempt to sign him ahead of the likes of Bayern Munich and RB Leipzig.
Man United 'keen' on Simons
The report claims that Simons is unlikely to stay at PSG this summer, and Leipzig are determined to secure his signature after a successful loan spell last term.
However, Bayern are also thought to view the Dutchman as a priority target during the current window.
Simons scored 10 goals and registered 15 assists in 43 appearances during a loan spell at Leipzig during the 2023-24 campaign.
The attacker was then in strong form for his country at Euro 2024, scoring once and providing three assists in six appearances at the competition, as Netherlands reached the semi-finals.
Simons arrived at PSG from Barcelona in 2019, but he has only represented the French champions on 11 occasions in all competitions, with seven of those matches coming in Ligue 1.
Man United are 'pushing' to bring in Ugarte
Ugarte is believed to be Man United's leading midfield target this summer, and the Uruguay international is allegedly keen on a move to Old Trafford.
The defensive midfielder only made the move to Paris from Sporting Lisbon during the summer of 2023, and he represented the Ligue 1 team on 37 occasions last term.
A recent report claimed that Man United have already come to an agreement with Ugarte over personal terms.
However, the 20-time English champions have work to do before a fee can be agreed, with a loan deal thought to have been ruled out despite the recent speculation.
PSG are believed to be determined to sign Joao Neves from Benfica this summer, and the sales of both Ugarte and Simons would help them to wrap up a deal for the Portuguese.