Moyes and Mourinho both coached Rooney during his period at Old Trafford, the Scot overseeing the striker's breakthrough at Everton too, and both managers believe the 32-year-old can be a success in America.
Kenwright confirmed at Everton's end of season awards that Rooney had taken a sizeable pay cut to return to his boyhood club last summer, and described negotiations for that deal as his "greatest and shortest".
"So I wouldn't consider anything on the cards on the moment".
However, if there are indications Big Sam is going to be replaced - Moshiri is said to still be uncertain about exactly what direction to take over a manager for next season - then he will wait to see who the replacement would be, and listen to his plans.
Allardyce muttered darkly about not being able to play him alongside Gylfi Sigurdsson, Everton's other marquee summer signing, while at the same time complaining that Rooney did not get into the box enough.
"We have not been in any hard situations with me". As to clarity of whether Wayne is leaving or staying I'll find out when he comes in for training today.
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Edmund will next face Canadian teenager Denis Shapovalov , who achieved a 6-4 6-4 win over compatriot Milos Raonic . Second seed Alexander Zverev beat Argentina's Leonardo Mayer and will now do battle with John Isner .
Rooney missed last week's draw with Southampton because of a minor knee injury, and is also set to sit out Everton's trip to West Ham on Sunday.
"How as a manager can you guarantee anybody to play?"
"Wayne's got a different physique", said Ferguson when Rooney broke Sir Bobby Charlton's United goal record.
The Washington Post reported on Friday that D.C. United are prepared to pay Rooney an annual salary of $5-8m (£3.7-5.9m).
"He appears to be level-headed and is one of those players who has not got carried away with it and I think that is probably why he has done so much, and played so well and achieved so much".
However Allardyce insists that Rooney has not asked to leave Everton and dismissed suggestions of a potential fallout between the pair. "I have a one-year contract", he said. "I don't want to create the headline".
Asked about planning for next season, the manager replied: "I've already done it".