The 26-year-old has been a hit for Villarreal this season and United scouts have been present at their recent games.
United could make a move for the striker at the end of the season.
“We have still not received any formal offers,” Villarreal president Fernando Roig said.
“We are calm and the interest is normal because Villarreal look to be developing a big season.”
“My mission is to play and to score goals,” Nilmar said.
“I do not enter into this speculation although I am flattered by the rumours because it is a sign that I am reaching a good level on the pitch.”