Moyes officially began his job as United manager on Monday, marking the start of a new era for United following the retirement of Sir Alex Ferguson in May.
The former Everton boss is now ready to end the ongoing uncertainty over Rooney's future and Sky sources understand Moyes plans to meet with the England striker on Wednesday.
Rooney has been heavily linked with a summer move away from Old Trafford - although United insist the 27-year-old is not for sale.
Moyes will have just over a week to settle into his new role before the Premier League champions head to Thailand for the first leg of their tour of the Far East and Australia.
His first game in charge will come on 13 July, when United take on the Singha All Stars in front of a sell-out 48,000 crowd at the Rajamangala Stadium in Bangkok.
But his first move as manager was to appoint Steve Round as his assistant manager, reprising their relationship at Goodison Park, with Chris Woods joining the staff as goalkeeping coach and Jimmy Lumsden taking on a coaching role.
Commenting on his backroom appointments, Moyes told United's official website: "I have worked with Steve, Chris and Jimmy for a number of years and I am delighted they have decided to join me at this great club.
"They bring great qualities in their respective fields and I know that, like me, they feel that this is a challenge to relish. I have great faith that together, we can build upon the success this club has enjoyed over many years."
Executive vice chairman Ed Woodward said: "I believe with David and his new team in place, along with our current backroom staff, we can now start preparing for the new season ahead.
"This is an exciting and challenging time for the club and I have great belief that David and his team will have all the energy and attributes needed to help this club continue in its long-standing traditions."
Moyes can now start building up to the opening game of the Premier League season against Swansea City on August 17, although there are several other key dates in his diary over the first few weeks of his United reign.
There are a number of challenges in store for the new manager and he will have a fairly full in-tray to work though as he settles into the role.
The club confirmed a new regional partnership, with Thai telecommunications company True Corporation Plc to be an associate match sponsor of the All Stars fixture.