MLS outfit DC United are interested in England's record goalscorer but as of Thursday he has yet to tell Toffees hierarchy he wants to leave.
Reports indicate Rooney's move will be completed when the MLS mid-season transfer window opens on July 10.
The club now lie bottom of MLS's Eastern Conference after winning just one of their opening seven games of the season.
Rooney is the all-time leading scorer for the English national team and Manchester United.
"There have been rumours about Wayne going overseas, China or America".
However, they also add that nothing has been signed yet, meaning it's still possible Rooney could prolong his second spell at Everton, the club at which he began his career.
DC United, along with MLS, have worked hard to come up with a package that would suit Rooney - and the league have helped as they see the prospect of such a huge name in the game playing in America as a huge asset.
Everton's Wayne Rooney is waiting to see what happens with the club's managerial situation before deciding what he does with his future, according to the Guardian.
But it has also been suggested uncertainty over manager Sam Allardyce's position could mean Rooney may stay at the club.
"I really enjoyed him at Everton, he was very young then, and at Manchester United he helped me a lot".
Back then he talked about how he wanted to play a part in Everton winning silverware after a long trophy drought, dating back to their 1995 FA Cup win.