The daily newspaper state that United are interested in the Germany international however, Besiktas are also looking to make his loan spell permanent at the end of the season.
The Express go onto say that Wolfsburg are also in the race to bring the 30-year-old back to Germany.
Gomez has 27 goals in all competitions for the Istanbul giants this season including 25 in the league.
Gomez has also scored six times and provided two assists in his last five league games. The goals have come at a critical point in the title race and have secured Besiktas a six point lead at the top of the table with two games left.
The Black Eagles take on Osmanlispor in the Turkish Super Lig this weekend know a point will clinch the title.