Rooney, back at Carrington on Wednesday after his summer break, was due to have medical tests and stayed for just over three hours before departing.
Moyes was also on site in his third day as United manager and it is understood he and Rooney are still planning to meet on Wednesday or at the latest on Thursday.
Rooney verbally requested a transfer in May, according to outgoing boss Sir Alex Ferguson, and Chelsea, Arsenal and Paris St Germain have all been linked with a summer move for the player.
But Rooney is 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 to the Premier League title later that season.
But Ferguson's former assistant Mike Phelan, who left United earlier this summer, has questioned whether the 27-year-old really wants to stay this time.
He said: "Wayne is at the greatest club you can be at.
"Why would you want to jeopardise that, unless you want a fresh challenge and you feel that challenge isn't being met at Manchester United?"
Sky Sports expert Gary Neville has also this week warned Rooney against quitting Manchester United during the transfer window.
Neville said in an interview with Talksport: "I played with Wayne for many years. He's a fantastic footballer.
"Personally, with my allegiances, I'd never recommend anyone leave United, because I believe it is a great stage to play football and you can achieve what you want there."
Neville added: "I've seen David Beckham and other big players leave United and it really is something that comes down to the individual and the club.
"I've seen Ryan Giggs, when he was 27, linked to Inter Milan, Juventus and AC Milan and stay."
However, players from rivals teams have insisted they would welcome the chance to play alongside the England international.
Chelsea goalkeeper Petr Cech told Sky Sports News: "I could see him in a Chelsea shirt. Players can change shirts and obviously he had a fantastic career with Manchester United and sometimes players need new challenges.
"Sometimes the consequences are the way that you are looking for the new challenge and change of the shirt."
Arsenal's Jack Wilshere believes a move for Rooney could help the Gunners end their long wait for silverware, saying: "If it happens, it would be amazing.
"He is the type of player who can win you trophies - and just to see his name on the team sheet brings fear to the opposition. We could do with a little more of that."