Manager Gary Locke is in England trying to secure the services of a keeper as they wait on the results of a scan on Jamie MacDonald, who was injured in Saturday's 2-1 win over St Johnstone.
Both Conor Brennan and Oliver Davies are unavailable.
"It's a huge worry for us at the minute," said Locke. "His (MacDonald) ankle is badly swollen."
MacDonald was replaced on Saturday by Brennan but he is cup-tied, having played for Stranraer in a previous round.
Loanee Davies is injured leaving Locke desperately short of options.
Kilmarnock loaned teenager Devlin Mackay to Derby County on transfer deadline day and the terms of the cross-border switch mean he cannot be recalled.
"We had an injury to Oliver Davies who was the back-up keeper, so he's had to go back to Swansea which is a bit of a disaster for us to be fair," Locke told the Kilmarnock website.
"We're trying to work on one or two things at the moment because Devlin's down at Derby and we're not allowed to call him back.
"It's a big problem at the minute, a big headache for myself, so we're trying to get something sorted before Wednesday."
Kilmarnock face a goalkeeping crisis ahead of Wednesday's League Cup tie against Hearts.