The Turkish newspaper AMK claims that five European clubs are involved in the race including the Manchester duo.
Gomez, who has been in phenomenal form for the Black Eagles this season has been heavily linked with a big-money move away from the club.
The powerful striker joined the Black Eagles on a two-year loan from Fiorentina over the summer and has hit the ground running at his new club.
Gomez also earned himself a recall to the Germany national team and scored his first international goal since 2012 against England in a friendly last month.
Gomez is in great form for the Istanbul giants having scored 26 times this season and surpassing the all time record for goals scored in a league campaign which stood at 21.