Both sides began their league campaigns with draws on the opening weekend of the season and they will be keen to get a first win of the season under their belts.
Following relegation back to League One in 2014, Paul Dickov's side failed to return to the Championship and make it four straight yo-yo seasons as they finished 13th, eight points behind the playoff places.
So far this summer Dickov has signed six players, and four of them - Thorsten Stuckmann, Aaron Taylor-Sinclair, Richard Chaplow and Andy Williams - started on Saturday as they had one of the most bizarre starts to the season imaginable.
Bury were the visitors to the Keepmoat, and after a goalless 90 minutes there was high drama in injury time as Harry Forrester accidentally volleyed the ball into the net from near the halfway line when trying to return it to Bury after they had kicked it out of play.
A bit of handbags broke out between the two sides before Donny sportingly allowed Leon Clarke to walk the ball in from kickoff so the match ended in a 1-1 draw.
Donny have a decent recent record in the League Cup first round, winning their first-round tie the last four years. Last year they beat Watford on their way to the third round, where they fell 2-1 to Fulham.
Recent form: D
The former Brentford and Wigan Athletic boss has been bold with his signings after the Whites had their transfer embargo lifted, and they got off to a good start on Saturday.
Newly-relegated Burnley were the visitors to Elland Road for a televised fixture and Leeds impressed in a 1-1 draw against Sean Dyche's Clarets, with late goals from Mirco Antenucci and Sam Vokes arriving after a goalless, but entertaining first 82 minutes.
It was an encouraging display from a Leeds side who have finished between 13th and 15th the last four seasons in the Championship and are desperate to get out of their mid-table rut.
Leeds have never been knocked out in the first round of the League Cup since its inception in 1960, a run of 55 straight years making it into at least the second round.
Last year they lost to Bradford City in the second round, with their best recent run in the competition when they lost to Chelsea in the 2012-13 fifth round.
Recent form: D
Rosler is sure to make a host of changes to the side that started against Burnley, with this the first of four games in 10 days for the Whites.
Dickov, meanwhile, could also make changes, but new signing Dany N'Guessan will not be making his debut as the club continue to nurse some knocks he picked up in pre-season.
Gary MacKenzie could make his full debut, though, after sitting out the 1-1 draw with Bury.
Donny possible starting lineup:
Marosi; McCulloch, MacKenzie, Butler, Taylor-Sinclair; Coppinger, Chaplow, Wellens, Forrester; Main, Tyson
Leeds possible starting lineup:
Turnbull; Wootton, Cooper, Bamba, Taylor; Murphy, Adeyemi, Phillips; Antenucci, Erwin, Doukara
Head To Head
The clubs' last meetings were in the 2013-14 season when Donny were relegated from the Championship. Rovers won the last encounter 2-1 at Elland Road, but Leeds had won six in a row before then.
This is the third time in five seasons that the two sides have been drawn against each other in the League Cup. Both ties in 2011 and 2013 were also played at the Keepmoat, with Leeds triumphing 2-1 and 3-1 respectively.
We say: Donny 1-2 Leeds
Despite the fact that Rosler will make several changes to the side that started against Burnley, there are still plenty who will want to impress for the away side and they should prove too strong for Donny.