The Rugby Park side had to forfeit last week's Group E opener against Falkirk following a coronavirus outbreak, with the entire first-team squad told to isolate.
The Scottish Premiership club anticipate having around six senior players available.
The rest of the squad will be chosen from their youth set-up.
Manager Alex Dyer is expected to give a greater indication of who is available for selection at a media briefing.
Kilmarnock have announced they will be broadcasting Tuesday's match on their club TV platform, while BBC Radio Scotland will provide live commentary on a busy night of cup action.