New manager David Moyes is believed to be hoping to have talks with the England international about his situation at the club but no announcement is expected imminently.
Moyes, who has been busy sorting out his backroom staff, will take his first Manchester United training session on Thursday afternoon.
But the future of Rooney, who is reportedly of interest to Arsenal, Chelsea and Paris Saint-Germain, will also be high on his agenda.
Former United boss Sir Alex Ferguson claimed Rooney verbally requested a transfer in May but Rooney 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.
He played a full part in another successful title-winning campaign last term but was surprisingly left out of the starting line-up for a crucial Champions League match at home to Real Madrid.
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?"
A great stage
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."