The England striker is widely reported to have submitted a transfer request for a second time during his stay at Old Trafford.
The previous one, in October 2010, eventually saw Rooney perform a u-turn when a move to Manchester City looked on the cards. The latest has been met with the club's response of "Wayne Rooney is not for sale".
Rooney is 5/6 to leave and the same price to stay with the Leeds-based firm.
Big-spending Paris Saint Germain are the 9/4 favourites to secure the 27-year-old's services after attracting the majority of backing in betting on his next club, with Bayern Munich and Chelsea (both 7/2) considered his other likely destinations.
Chelsea's price has shortened after a move to Stamford Bridge was suggested by some newspapers.
A controversial switch to Manchester City is a 25/1 shot, with a return to Everton 50/1.
The news is another blow for United, who on Wednesday learnt of Sir Alex Ferguson's intention to call time on his 26-year reign at the end of the season, with betting suspended on Everton boss David Moyes being his successor on Wednesday night.
Moyes fell out with Rooney when the pair were both at Goodison Park but have since made up. Whether they would want to be reunited in a dressing room though remains open to question.
Sky Bet football trader Chris Spicer: "We already had betting open on Rooney's next club amid small rumblings of discontent, with PSG attracting most bets on his next club, but the heightened speculation has prompted us to offer odds on whether he'll stay or go, something we reserve for players whose futures are under major doubt.
"Coupled with Ferguson's impending retirement, the developments surrounding Rooney's future have forced us to reconsider United's chances of retaining the Premier League title, and we have now pushed them out from 13/8 favourites to 15/8, the same price as rivals City."