The England striker is widely reported to have submitted a transfer request for a second time during his stay at Old Trafford.
Big-spending Paris St-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, while a controversial switch to Manchester City is 25/1.
It serves as a successive blow for United, who 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.
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."