Mourinho is said to have decided that his team need a marquee name if they are to dethrone Manchester City as Premier League champions next term.
United finished a huge 19 points clear of their rivals last season.
And Don Balon say that, if PSG are unable to sign Mbappe, Mourinho is confident of luring him to United.
Where he fits in, however, remains to be seen.
If played up top, that would see him oust Romelu Lukaku, who scored 27 times following his arrival from Everton last summer.
Man Utd transfer news: Jose Mourinho is eager to sign Kylian Mbappe (Image: GETTY)
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PSG's Mbappe sent off after video referee decision
On the left, United’s options are well-stocked.
Alexis Sanchez, Marcus Rashford and Anthony Martial can all play there, meaning the arrival of another right winger is redundant.
The right is where Mbappe may be played.
But Mourinho is understood to want proven players this summer and the teenager, despite his insane ability, would represent a sizeable gamble.