This time, however, they would be wise to let it go.
Nevertheless, that doesn't stop the rumour mill churning. Martin Lipton at The Mirror wrote that the Blues will renew their pursuit of Rooney, in light of reports that the player has rejected new contract talks with United.
For his part, David Moyes remains unconcerned about the situation, stating to The Express that "I think we are fine. We are just moving on from the summer. It will be done in good course. The appropriate people will talk when the time is right."
Rooney has been one of the few bright spots in Moyes' first season in charge of United, and it's clear that the manager needs him right now.
It's important that Moyes is able to provide some stability through the transfer window in order to acquire new payers, while Rooney is likely to use the club's current league position as leverage to secure the maximum amount he can.
However, Jose Mourinho will be unwilling to overpay, as we saw in the summer. Chelsea failed to raise their bid of £25 million before the deadline as The Guardian reported that United finally took a stance that Rooney was not for sale—at any price.
If he was unavailable in August, then there's no reason for him suddenly to be for sale in January. Moyes needs him to continue his run of form and inspire his side to greater heights in the league, and the Glazer family could also step in and use their authority to assert that he is a Manchester United player.
Rooney is unlikely formally to hand in a transfer request unless there is a serious offer made by Chelsea. Despite the fact that they made two bids for him in August, neither could be considered anything more than a testing of the waters.
While Chelsea could use some more goals, it just makes no sense for United to sell him to a rival. At 28, Rooney isn't going to make the move abroad, so his only chance of leaving United is likely to be a move within the Premier League.
Rooney will obviously wish to play Champions League football, where he has 30 goals in 78 appearances for his current club. Chelsea will no doubt use that as bait with which to lure him to London.
However, it's not going to be up to Rooney. He is contracted until 2015 with the Red Devils and the club needs him too much to let him go. It's in his interest to accept that and continue to play well for Moyes and United.
If he does that, he will earn the big contract he wants at the end of the season. However, January is not the time to attempt to force his way out of the club—Mourinho would be better off looking elsewhere.