United closed Carrington for an initial 24 hours eight days ago and their Premier League games at Brentford and at home against Brighton were postponed.
A statement on the club’s official website read: “Manchester United’s players have started a return to training at Carrington, on a staggered basis.
“The complex was closed for first-team operations last week due to a COVID-19 outbreak at the club but opened again (on Tuesday) morning.
“Hence, this will now give interim manager Ralf Rangnick and his squad time to prepare for our next fixture – the Premier League meeting with Newcastle United at St James’ Park on Monday, December 27 (20:00 GMT kick-off).”
“Unfortunately, the games against Brentford and Brighton & Hove Albion were postponed as the club had no option but to request that the matches were rearranged.
“The Premier League board took the decision to call the fixtures off, based on guidance from medical advisors.”
It was reported four players and staff members had returned positive lateral flow tests following the 1-0 win over Norwich on December 11 and the results were confirmed by PCR tests a day later.
Those individuals were sent home before the rest of the squad trained outdoors, with the schedule adjusted to individual and non-contact sessions.
The club added: “On Monday, the Premier League issued a statement declaring the intention to continue with the festive programme, where possible, despite the impact of the Omicron variant of Covid-19.
“United are also scheduled to face Burnley next week, on Thursday, December 30, at Old Trafford (20:15 GMT kick-off) in our final outing of 2021.”