The 28-year-old has been attempting to speed up his recovery from a groin injury and will undergo tests ahead of the champions' visit to Stamford Bridge.
Rooney has been based in the beach resort of Sharm El-Sheikh and will now be monitored at Carrington ahead of the crucial clash at Stamford Bridge on Sunday.
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Rooney was with wife Coleen and his children in Egypt, as well as a United medical officer who was sent to monitor the forward's training. Moyes and United's medical team have received good reports back but believe that Rooney could still benefit from three to four weeks of proper rest away from training and matches.
"Wayne has done well in Sharm El-Sheikh and the early signs are good," a club source told Goal UK. "He will come back into Carrington on Wednesday and be assessed all the way up to the trip down to Chelsea."
United has been attempting to manage Rooney's injury by playing the striker intermittently and resting him one game at a time, but the striker has continued to complain about tightness in his groin.
"Wayne has a bit of a groin-adductor problem which we just think might need a little bit more time," Moyes told reporters ahead of United's 2-0 victory over Swansea on Saturday. "It looks as if we could bring him in but then he may have to drop out again, so we just want to nip it in the bud and see if we can get on top of it."