The report states that United scouts have been monitoring the 30-year-old this season and that Louis van Gaal has given the green light to sign him.
United boss Van Gaal recently praised Gomez which led to further speculation that a move for the experienced striker could be on the card.
“I was manager of Bayern, and there the striker was Mario Gomez, and he touched the ball nine times as an average in a game,” Van Gaal was quoted as saying by the Guardian.
Gomez has hit the ground running at Beşiktaş scoring nine times already this season and has attracted interest from Manchester United according to the Telegraph.
The 30-year-old was recalled to the Germany national team recently after impressing for Beşiktaş this season. The Black Eagles are currently first in the Turkish Super League two points clear of Fenerbahçe.