The Denmark international has been on the sidelines since suffering ligament damage in a challenge from Andy Carroll during the FA Cup contest with Championship side Reading at the end of January.
Ten Hag has revealed that Eriksen has made strong progress in his recovery, with the 31-year-old in line to return to the field at "some point in April".
"Yes, some point in April, he will be back. He is doing really well, really good in his rehab. The progress is very good and we have to see how that develops in the coming weeks," the Dutchman told MUTV when asked for an update on the midfielder.
Eriksen moved to Old Trafford on a free transfer last summer following his exit from Brentford, and he has been an important player for Man United this season, scoring twice and registering nine assists in 31 appearances.
Man United only have one more game before the end of March, which is Sunday afternoon's FA Cup quarter-final with fellow Premier League side Fulham at Old Trafford.
The Red Devils will then begin April against Newcastle United, before also facing Brentford and Everton in the league ahead of the first leg of their Europa League quarter-final against Sevilla on April 13.
As well as Eriksen, Donny van de Beek will again be missing against Fulham, with the Netherlands international out for the season with a serious knee injury, while Alejandro Garnacho is missing due to an ankle problem.
Antony and Anthony Martial are also major doubts, while Casemiro will start his four-match domestic suspension on Sunday following his red card against Southampton in the Premier League.
Ten Hag also revealed that Scott McTominay was a doubt for the clash with Fulham, having been unable to feature off the bench against Real Betis in the Europa League on Thursday.
"As you said, we just returned. We have to see, to see the doc. I have an idea but I have to see the progress with some players," said the Dutchman.
"About the last game, that is why I didn't bring him in, Scott McTominay, [as] he had some complaints. We have to see how that will progress in the coming hours and days."
Man United have already lifted one trophy this season, winning the EFL Cup at the end of February, while they are chasing silverware in both the FA Cup and Europa League.
A Premier League title challenge is not impossible but incredibly unlikely at this stage of the campaign, with the Red Devils instead focusing on a top-four finish, and they are currently third in the table, three points clear of fifth-placed Newcastle United.