Mourinho watches Gacinovic in Austria
The 22-year-old has burst onto the international scene with Serbia, scoring twice in his first three appearances for Slavoljub Muslin's side.
Mourinho was spotted in the stands, trying to go unnoticed by wearing a grey hat, as Serbia succumbed to a 3-2 defeat in Austria.
However, according to 'The Mirror', United's boss will face stiff competition from German champions Bayern Munich, while Arsenal have also registered an interest.
Gacinovic enjoyed a prolific spell with Serbian side Vojvodina in the Super Liga, scoring 11 goals in 10 games, but he has since found goals hard to come by following his move to Frankfurt.
He has scored four times in 51 appearances in all competitions in Germany, with one of those coming this season.