Darby, who produced a magnificent goal-line clearance at Colchester United on Saturday, is troubled with a tight groin, meaning he could miss City's second trip to stadiummk in eight days.
Should Darby miss out, it will be City's first game of the campaign in either the league or the cup without the skipper in their starting line up.
Mark Yeates is also doubtful for the third round tie after suffering further problems with his left shoulder during the Colchester match at the weekend.
With Alan Sheehan serving out the final game of his three-match suspension and Andrew Davies, James Hanson and Matthew Dolan all still sidelined, Parkinson admits that his options for the match are limited.
As a result, apprentices James Pollard, Callum Chippendale, Reece Webb-Foster, James King and Sam Wright have all been included in City's squad for the tie.
Parkinson said: "(Stephen) Darbs has some tightness in his groin and (Mark) Yeatesy still has a bit of an issue with the shoulder problem he's been having so we'll have to look at them both before naming our team.
"In terms of making possible changes, we are quite restricted with what we can do given the limited numbers we have available to us. We are down to the bare bones a bit.
"We will still pick the team which we think is the best for us though.
"There will be three or four of our youngsters on the bench on Tuesday which is great experience again for them.
"Most of them have travelled with us over these last two away matches (MK Dons and Colchester United). It will be encouraging for them to see that there is a definite link from the youth team through into the first team.
"I remember when we played at Wigan Athletic a couple of years ago in this competition and won there. We had some of the young lads on the bench that night as well.
"Tuesday is the final part of three long away trips for us in a week.
"We have to be happy with the points haul we have picked up from the first two but we want to finish it off with progression in the cup."