Cottagers coach Rene Meulensteen was impressed with 21-year-old Burn's composed performance in his senior home debut for Tuesday's 3-0 FA Cup third-round replay victory over Norwich.
And now the Dutchman has admitted Fulham will weigh up whether to send the former Darlington centre-back out on another loan, or pitch him into league action with the Cottagers.
Burn made 28 appearances in his loan stint at Birmingham in the first half of the season, before being recalled by Meulensteen on January 2.
Blues boss Lee Clark remains keen on another loan deal for Burn, but Meulensteen said he could very well keep him on hand instead.
"Dan's been a breath of fresh air. He did well in the Norwich away game," the Fulham manager said.
"Him staying here now is definitely something we're going to review, definitely.
"That's a different challenge from playing at home, but he's matured a lot in Birmingham where he had a very good loan spell.
"And next to Brede Hangeland he looked extremely comfortable.
"The only way that I keep them apart is that he's right footed and Dan's left footed.
"You work with him on the pitch - it's great for someone like Dan to have Brede coming back from that injury so they can work together.
"Dan is a very bright boy, he's not afraid to speak his mind, he talks, and that's the sort of thing you look at, and it was a very positive performance from him."
Meanwhile, Fulham face a Premier League investigation in light of Meulensteen's relevations on West Ham midfielder Ravel Morrison.
Meulensteen revealed Fulham had a bid turned down for the 20-year-old, claiming the England Under-21 cap wants to move to Craven Cottage.
Dutchman Meulensteen coached Morrison at Manchester United, and hinted his long-standing relationship would be at the centre of the coveted midfielder's desire to join him at Fulham.
"We got knocked back, it got rejected, and so we need to review it and move on," Meulensteen said.
"Yes we did make a bid. Yes I think he wants to come.
"I've known him for a long, long time, but the thing is this: we have to wait and see how the club takes it forward."
West Ham are understood to have made an official complaint to the Premier League, citing ruling T.8, covering public statements of interest in a rival club's player that act as an indirect approach.
On the pitch, Darren Bent's tidy finish and intelligent header to spark the move for the second goal offered hints of a return to form against the Canaries on Tuesday night.
Fulham's reward for the convincing victory is a fourth-round trip to Sheffield United on Sunday, January 26.
Meulensteen challenged the 29-year-old to keep repeating that level to force his way into regular selection contention.
"I thought he was excellent, and that's what we want him to do," Meulensteen said.
"He scored away from home in this round of the cup at Norwich, and he's scored again.
"The only way for Darren to get more and more of those performances in is to keep doing what he did there.
"If he does put that kind of performance in, the more and more likely it is that we're going to use him.
"That's what you want as a manager - you want the players to push each other and give you decisions to make."