The FA has been in regular consultation with clubs, including Albion and key stakeholders from the Barclays FA Women’s Super League and the FA Women’s Championship throughout the Covid-19 pandemic.
This includes a detailed examination of the financial, logistical and operational challenges faced during this pandemic.
Albion's Premier League squads started non-contact training on Tuesday but the WSL and women's second-tier teams are not expecting to do so this season.
Hope Powell's Brighton Women were ninth in the WSL league standings with 13 points from 16 matches when the league was suspended.
Manchester City Women led the way at the top on 40 points, just one point ahead of second Chelsea placed Chelsea, who had a game in hand on the leaders.
Liverpool Women were bottom on six points and were in the relegation zone when play was halted.
A statement from the FA read: "Following an assessment of the protocols required to return to football and feedback from clubs, which is crucial to any decision-making process, it is clear that there will be significant challenges in completing the 2019/20 season.
"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 Barclays FA Women’s Super League season.
"Our overriding ambition is to give the clubs, players and stakeholders in the game the support and clarity they need during these challenging circumstances, and to help and enable women’s football to continue to thrive in the future."
A message from the Editor, Gary Shipton: In order for us to continue to provide high quality and trusted local news, I am asking you to please purchase a copy of our newspapers.
With the coronavirus lockdown having a major impact on many of our local valued advertisers - and consequently the advertising that we receive - we are more reliant than ever on you helping us to provide you with news and information by buying a copy of our newspapers.
Our journalists are highly trained and our content is independently regulated by IPSO to some of the most rigorous standards in the world. But being your eyes and ears comes at a price. So we need your support more than ever to buy our newspapers during this crisis.
Stay safe, and best wishes.