The Leeds boss has been discussing the former Manchester City youngster, currently on trial with the Whites.
Indeed, the 21-year-old former Manchester City youngster is on trial with Leeds, as confirmed by Rosler recently.
And Drury has integrated well, according to the Leeds boss, showing promising signs while training with United.
A final decision on his future is yet to be made but he will continue to work with the club for a while to come before he can be given a clear indication on whether he will be offered a deal, the manager has revealed.
He told BBC Radio Leeds: "He's still here, I spoke with him yesterday. We will have a look at him and another talk at the end of next week, before we go to Austria.
"Then we can give him a clear indication - Adam's fine with that. He's integrated himself well and he's showing promising signs."
Leeds play Harrogate Town later tonight, with Rosler suggesting he will use two different teams and styles in each half against the non-league side.
Interestingly, Drury plays the same role as Sam Byram - at right-back and at right-wing. Naturally, though, any potential signing could just be as cover.
Leeds' transfer plans may also have been affected - in terms of the Yorkshire club needing to speed up their search for a new midfielder - by Luke Murphy's recent injury.