United manager Sir Alex Ferguson has been tracking Valencia for several months and Whelan admitted the Premier League champions had made an initial offer.
A deal for Valencia, who is valued at around £16 million, would mark the start of Ferguson's attempt to revitalise his squad after the imminent departure of Cristiano Ronaldo to Real Madrid for a world record fee of £80 million.
"They [United] have been in touch with us and we will be starting negotiations very shortly, I would imagine," Whelan told Sky Sports News.
"United have been in touch with us over Antonio for the last two or three months, expressing an interest and actually putting cash offers on the table.
"Those things have got to be picked up now. I think they were waiting to see if Ronaldo actually went to Real, which has happened. Things will develop over the next seven to 14 days.
"Sir Alex had him watched practically every, single match last year. He has got a very strong interest in him. We are just sat on the fence now.
"We are not desperate to sell Antonio, I'm telling you. If I can keep that lad, I'm going to keep him. He is one brilliant player.
"So there is no pressure on me, or our football club to sell him. If Man United don't want to make a [written] offer, I'll be delighted and we will have him in our team next season."
Meanwhile, Wigan have apologised for the embarrassing failure to unveil new manager Roberto Martinez on Thursday.
Martinez, 35, was due to be announced as Steve Bruce's successor after agreeing a contract with the Latics and was at Wigan's stadium waiting to meet the media.
But the Spaniard's move from Swansea was held up after the Championship club demanded compensation for Martinez's assistants, leaving Wigan to cancel the press conference and insist the deal would still go through soon.
"Wigan would like to apologise to the supporters for the delay," a statement read. "The club would like to stress that talks with Roberto have been extremely positive and personal terms have been agreed.
"We are confident to resolve the issue by early next week. We have already agreed a compensation package to Swansea City for Roberto and talks are ongoing between the clubs about the backroom staff.
"Once these issues have been resolved we will be able to unveil Roberto as new manager and get on with the job of preparing for next season."