Darlington were paired with Leeds United in the second round of the Johnstone's Paint Trophy when the draw was made on Saturday.
Like Quakers, Dennis Wise's side were handed a bye in the first round of this season's competition so their trip to the Balfour Webnet Darlington Arena will be Leeds' first game in the competition.
The game, to be played in the week commencing October 8, represents a rare home draw for Darlington as it is only their third in their last 13 cup ties.
Despite competition rules, which state clubs must field players who have appeared most often in first-team games this season, Penney hopes to make some changes for the clash.
"It would have been nice to have had Leeds away, but we're happy with the draw," said Penney.
"I'm worried about the restrictions because I think you have to play at least six players who have played in most of your games.
"We have got a big squad and it would be nice to change it around a bit to give some players a rest.
"There are people like Gregg Blundell and Ian Harty who need games and need 90 minutes so we'll look forward to that."
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article