The Football Association says it is “continuing to consult” with clubs on the “possibility of terminating” the Women’s Super League season.
Club representatives and the FA are understood to have held a meeting on Monday, but no final decision on how to conclude the campaign was reached.
An FA statement said it is “clear that there will be significant challenges in completing the season”.
No WSL fixtures have been played since February because of coronavirus.
The outcome of the Women’s Championship, the second tier of women’s football in England, is also still to be decided.
It is understood that, during a video call with player representatives on Friday, players urged league officials to reach a verdict as quickly as possible to “end the uncertainty”.
Monday’s statement from the FA added: “Our primary concern has always been for the welfare of the clubs and players; and working collaboratively to identify the most suitable and appropriate way to return to football.
“Every possible scenario has been meticulously analysed and evaluated in order to find a solution to meet the unique demands of the women’s game.
“We are continuing to consult with the clubs on the possibility of terminating the 2019-20 season and, in the event it is decided that this appears to be the only realistic way forward, to seek views on the most appropriate sporting outcome for the season.
“This includes identifying entries for the 2020-21 Uefa Women’s Champions League, which would be based on sporting merit from the 2019-20 Women’s Super League season.”
How does the table look?
The top two teams in the WSL would ordinarily qualify for the European competition in the following season.
Manchester City hold a one-point lead at the top of the WSL table, but second-placed Chelsea have a better points-per-game ratio, so if an average points-per-game system was chosen to determine final league positions, Chelsea would leapfrog City.
Arsenal are third and, like Chelsea, have a game in hand on the leaders, but are four points behind City.
At the bottom, Liverpool occupy the WSL’s only relegation spot, but it has not yet been decided whether or not a team will go down this summer, nor what will happen regarding promotion from the second tier.
Aston Villa are six points clear at the top of the Championship, ahead of Sheffield United in second, with six rounds of games outstanding.
The seasons in tiers three to seven of the women’s game were formally cancelled in April, with all results declared null and void.