Jose Mourinho’s side have reportedly watched Forsberg, who has impressed for a Leipzig side that is currently second in the Bundesliga.
The Sweden international has scored three goals and provided two assists in 14 matches in all competitions this term.
Jose Mourinho was said to be watching him from the stands as he put in a good display for Sweden against Italy last week, but the 26-year-old is paying no mind to links with the Red Devils.
The Manchester Evening News quote him as saying: "I also read that in the papers, my focus is on RB."
Forsberg was a member of the Sweden squad that beat Italy to qualify for the World Cup, and he remains amazed by his side’s accomplishment.
"Nobody thought we were capable of this," Forsberg said. "The group was already difficult. France and Netherlands are two really good teams. They said we ran out of luck after the playoffs draw, but we made it despite all that.
"I believe that we wanted the ticket [to Russia] by all means, and we played as a team believing in its chance. It's a dream come true. There is no bigger or better competition. The best players in the world are there and we are part of it."