Should Rooney receive assurances that he is central to the new manager's plans, he could remain at Old Trafford.
On Wednesday night, a spokesman for United insisted Rooney, who made a verbal request to leave, was not for sale.
The 27-year-old still has two years of his contract to run, although, at this stage, United do not plan to offer him a new deal.
Moyes, who has signed a six-year contract with United, handed Rooney his Premier League debut as a 16-year-old in August 2002.
But the player left Moyes and his hometown club Everton in August 2004 in a deal worth an eventual £27m. He has since scored 197 goals in 402 appearances for United, winning five league titles, two League Cups and a Champions League.
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