The Portugal international is said to have been a long-term target for the Red Devils, and those rumours have only intensified since his Portuguese compatriot, Jose Mourinho, took charge at Old Trafford last week.
Additionally, the 22-year-old and the former Chelsea manager share the same agent – Jorge Mendes – although Gomes says he wants to focus on Portugal’s Euro 2016 preparations rather than a transfer away from Spain.
“We are focused on Portugal and that is what we are interested in speaking about,” he told Portuguese newspaper O Jogo.
Mourinho is keen to strengthen a United midfield with question marks over the fitness of Bastian Schweinsteiger, and whether Morgan Schneiderlin is a long-term fit after a disappointing debut campaign for the club.
Gomes has made 77 appearances in all competitions for Valencia, scoring nine goals.