The 25-year-old centre-back has featured in a Blades shirt for just 10 games, but Egan believes he has benefited from working with United coaching duo Chris Wilder and Alan Knill.
The Republic of Ireland international – who earned his third cap against Poland this month – has been a key figure in United’s defence alongside Jack O’Connell and Chris Basham, since arriving at Bramall Lane from Brentford.
“I think I have improved already since I came here,” said Egan.
“The manager and Knilly, I heave learned a lot from them, and improved as a player.
“Continuity at the back has been important. We have all been really consistent so far. Hopefully, we can keep being a good defensive unit, to build the team on.
“Overall, we have had a really positive start, and are up around the top of the table, where we want to be.
“Obviously, since the first couple of games – where we were probably still gelling a bit – we have managed to turn things around and won a lot of games.”
Egan swapped Brentford for the Blades, hoping the move would improve his chances of reaching the Premier League.
He added: “My ambition is to get to the Premier League. I wouldn’t have come if that didn’t match the club’s and manager’s ambitions.
“For most players in the Championship, that’s their ambition, too. I am no different to them.
“You have to take each game as it comes in this league, because it changes so fast.
“Our belief is we want to be up at the top end of the table all season. To do that,we have to keep winning games.
“The international break probably came at the wrong time for us (after beating Aston Villa).
“We went to Bristol City, played really well and didn’t get anything out of the game.
“We got a draw against Birmingham City, and looking to get back on track against Preston, a tough side to play in this division, it was a really good win for us.
“Our focus now is on Millwall on Saturday, to go there and get three points. It’s a tough place to go.”