The Danish international midfielder, 31, was expected to be out until May with an ankle injury.
But he has returned to training and there is optimism around the club that he could be available soon.
While Eriksen is expected to miss United‘s next two league games away to Newcastle and at home to Brentford a place on the bench for the visit of Everton on April 8 is now on the radar.
Speaking during the international break Eriksen said: “It is going well. I have just started being outside with football boots on.
“And then we take it from there, that is the next step. I have been in the gym for some weeks now and now it is time to do the next rehab session outside.”
The former Spurs and Inter Milan midfielder joined United last summer as a free agent after a short spell with Brentford.
He was in top form until he suffered an ankle injury during the FA Cup win over Reading on January 28 after a heavy challenge from Andy Carroll.
His return will be a huge boost for manager Erik ten Hag as the Red Devils start their run in with a Cup treble to aim for and a top four spot in the Premier League.
Ten Hag will be missing Casemiro for the next four league games due to his second red card of the season against Southampton on March 12.
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Marcel Sabitzer is also an injury doubt after suffering a knee injury on international duty with Austria.
There is good news surrounding Marcus Rashford who has been back in light training at Carrington.
He withdrew from the England squad after picking up a knock against Fulham before the international break.