Rooney spent around seven hours at the Carrington training complex before leaving just before 4pm - it is not known whether he took part in Moyes' first training session as United boss.
Moyes has spent the day sorting out his backroom staff with Ryan Giggs and Phil Neville both appointed to his coaching team but it had been expected that a meeting with Rooney would also take place.
The 27-year-old's future has been the subject of speculation since former United boss Sir Alex Ferguson left him out of the starting line-up for a crucial Champions League match at home to Real Madrid.
Ferguson subsequently claimed Rooney verbally requested a transfer but the players has yet to comment publicly on the speculation, amid reports he disputes Ferguson's version of events.
A previous transfer request in the autumn of 2010 ended with Rooney signing a new deal at Old Trafford and helping the club win the Premier League later that season.