The Scot is at the home of the champions and will meet staff and be given a tour of the facilities as he prepares to take over from Sir Alex Ferguson.
The Scot drove into Carrington just at before 9am on Monday to meet the club's staff and medical team. He will also receive a tour of the training center and get briefed on its facilities.
Moyes does not officially take charge of United until July 1 but is taking the reins already following his final game as manager of Everton on Sunday, which ended in a 2-1 defeat at Chelsea.
Ferguson officially retired after United’s sensational 5-5 draw with West Brom and has now stepped aside to allow Moyes control, with the former Preston boss arriving on a six-year contract.
Moyes’ contract with Everton expires on June 30 but the Toffees are understood to have given the 50-year-old permission to begin the transition into his new role.
Moyes, who was confirmed as Ferguson’s successor earlier this month, said after Sunday’s match that he will also spend time at Everton’s training ground this week to ensure everything is in place for the new Merseyside club’s manager.
"I will go into Finch Farm some of the days next week and make sure things are in place for whoever the incoming manager is,” said Moyes.
"I would like to be remembered for doing a hard working honest job because that is what the football club stands for."