It is understood in an informal chat with Sir Alex Ferguson a couple of weeks ago, Rooney suggested it would be better if he made a fresh start away from Old Trafford.
United have rejected the idea out of hand and insisted: "Wayne Rooney is not for sale."
However, it is thought Rooney has been unimpressed at being asked to play out of position during the latter weeks of the season and with Robin van Persie impressing in his debut campaign, wondered whether he had a future at United.
Ferguson's impending departure, coupled with Moyes' impending arrival, brings Rooney back together with his first boss at Everton.
The rift caused by comments Rooney made about Moyes in his autobiography has now been healed.
However, with two years remaining on his contract, United must make a move or risk Rooney electing to let the deal run down and leave for nothing.
That is an unpalatable prospect, yet there have been suggestions Rooney will be asked to take a pay cut from the mega deal he signed in 2010 - days after handing in a transfer request - which would not go down well either.
Ferguson had not forgotten how Rooney effectively held the club to ransom in the aftermath of Cristiano Ronaldo's exit, something he vowed not to let happen again.
Moyes has none of that baggage. However, the Scot will be mindful of the need to keep Rooney fully motivated. And with the likes of Chelsea and Paris St Germain offering a potential way out, Moyes could easily elect to sever ties with the England man for a second time.
Meanwhile, reports suggested that Rooney had removed 'Manchester United player' from his Twitter biography and replaced it with 'NikeUK athlete'.
His representatives insisted no change had been made recently and it later emerged that a number of other Nike-sponsored players - including United team-mate Tom Cleverley - had made similar changes to their social media biographies some months ago.