The News of the World says United's boss is believed to have made an offer for the Spanish international in the last week of the summer transfer window.
Fergie could even do a deal which sees the player stay in Spain until the end of the season to avoid paying an inflated fee for him after the World Cup.
Silva has a contract at the Mestalla until 2013 which is worth around £50,000-a-week.
And the Spanish club are keen to do business as they attempt to ease financial worries caused by an impending move into their new 82,000-seater stadium.
"It is true that there was a bid from a big English club," said Silva. "If it was only a question of money then I would have accepted the move.
"Things can change in the future but right now I am happy in Valencia and I did not have sufficient motive to leave."