United closed Carrington for an initial 24 hours eight days ago and their matches at Brentford and at home against Brighton were subsequently called off.
“Manchester United’s players have started a return to training at Carrington on a staggered basis,” the club said in a statement.
“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.”
The Premier League announced on Monday that it would continue with its schedule despite widespread coronavirus outbreaks, which forced the postponement of six of the weekend’s 10 fixtures.
The English top flight reported 90 new coronavirus cases among players and staff last week — a big leap from 42 in the previous week.
United are currently sixth in the Premier League table having played two games fewer than most of the teams above them.
They are due to travel to face struggling Newcastle next Monday, with a home game against Burnley three days