Brighton Women's manager Hope Powell says all players and coaches "want the Women's Super League season to finish" but the health and safety of everyone involved is "absolutely paramount".
The Football Association is determined to complete the campaign but wants it concluded by early August.
Voiding the 2019-20 season was one of several options discussed over a conference call on Friday.
WSL bosses said the season will only resume if and when it is safe.
Friday's conference call came after Thursday's announcement that tiers three to seven of the women's game are to end their seasons immediately, with all results expunged, because of the coronavirus pandemic.
"We don't have a crystal ball so nobody knows how long it is going to last and when the season can resume," said Powell. "I think everybody from an athlete and coach perspective, of course, wants the season to finish.
"We need to leave it for those decision-makers who are in constant contact with medical advisors. They will make the best decision and base that on people's health and wellbeing and safety, I am sure."
Brighton defender Felicity Gibbons said all clubs would have to "accept whatever the outcome is" but suggested finishing the season "would probably be the most fair outcome".
"There's a whole bigger picture at the moment and health and safety is more important than football," she added.
The postponement of football until at least 30 April has left question marks on the financial implications of clubs in the WSL with a number of players on short-term contracts which are due to expire before anything resumes.
Asked whether Powell has concerns about this, she said: "So far Brighton have been really supportive. This is something that will affect everybody at every club but we wait and see.
"It is not my decision [on whether to extend player contracts]. I don't own the club. I'm governed by people above me but I know the club will do everything within its power to ensure jobs are safe and that is the best they can say."
Women's players have struggled to get access to gym equipment - England international Beth Mead put out a call for assistance on social media - but Powell says Brighton have delivered stationary bikes to every player at the club.
"They [Brighton's players] get whatever they need - bands, footballs, cones - whatever the club were able to get," said Powell.
Gibbons added: "I don't have a luxury swimming pool or a home gym but you've just got to make the best of a bad situation. I've got equipment which I can make work for both an upper and lower body gym session and gym sessions are quite easily adaptable."