Swansea City chairman Trevor Birch says the club could lose close to £1m from season ticket refunds.
The Championship is set to resume in June behind closed doors.
Swansea have four home games remaining and have told supporters they are eligible for partial refunds of season tickets and hospitality.
"However, I am sure you understand clubs are facing a very uncertain financial future - and we are no different," Birch said in a statement.
Championship clubs are due to start training on Monday following safety guidance and protocols issued by the EFL.
Swansea and Cardiff City will both have to wait for the green-light from the Welsh Government, with league officials having been in "constructive" talks with ministers.
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A 13 June date has been suggested for a return to fixtures without fans, but Birch has pointed out the financial cost from potential refunds.
He has asked fans to consider options, one of which would be streaming remaining games at home.
"The club estimates that the cost of partial refunds for 2019-20 season tickets and hospitality will amount to just under £1million which will put even greater pressure on the club's cash flow during these difficult times and for future operations," he said.
"I am acutely aware that many families are struggling financially during the pandemic - and all of us at the club thank fans for their patience."