The Red Devils are expected to spend on a centre-forward this summer amid the poor form of Rasmus Hojlund and Joshua Zirkzee upfront.
Hojlund and Zirkzee have failed to adapt to the intensity of the Premier League. They have netted just six goals in the top-flight this season.
It is now reported that United have established contact with the representatives of Mateta, who has 17 goals to his name this term.
The Frenchman has become one of the best strikers in the Premier League over the last 18 months. He could secure a bigger challenge for next season.
His current deal concludes in June next year and it has been reported that he could be signed for around £40m during the next transfer window.
United could make a serious approach for his services depending on manager Ruben Amorim, who has the final say on transfers.