The 28-year-old has stepped up his recovery from the toe injury he suffered just over six weeks ago.
Egan has been sidelined since dislocating his toe in the defeat at West Ham on February 15, which saw all three of the Blades' first-choice central defenders out through injury.
With Chris Basham and long-term absentee Jack O'Connell also out, wing-backs George Baldock and Enda Stevens have played as makeshift centre-backs in recent weeks – although Stevens caused the Blades another injury scare this week when he returned early from international duty with the Republic of Ireland.
Interim boss Paul Heckingbottom, in charge until the end of the season following Chris Wilder's departure as manager just before the international break, said: "He (Egan) is back in training and we are hoping we can build him back up as quick as possible so he can play.
"It will be a case of building him up and then playing 90 minutes. Enda came back but he should be OK to train and Egs (Egan) is coming back to be built up to playing 90 minutes."
There was mixed news elsewhere regarding the Blades' injury issues.
Sander Berge could only be a fortnight away from a comeback, after more than three months out following a hamstring operation. But Basham and club captain Billy Sharp will miss Saturday's game at Elland Road.
Norwegian midfielder Berge was called up by his country for the recent internationals, despite being injured, and was pictured joining in training as he steps up his rehabilitation.
"Sander is still a couple of weeks away," said Heckingbottom, who had a short spell as Leeds manager in 2018.
"He is out on the grass building up his speed and he is still doing his own personal rehab. Once he is back up to speed, we will be able to integrate him back with the squad.
"I'm afraid Sharpy's was quite a significant muscle injury, and he will be a few weeks, while Bash was a strange one. He was playing right up until the Chelsea game (on March 21) and we have not managed to get him on the training ground yet. Hopefully we will have him available in the not too distant future."
The Blades head to Elland Road bottom of the Premier League table and 14 points adrift of safety, with only nine matches remaining to pull off the greatest of escapes.