The BBC said Premier League clubs have agreed to conduct a feasibility study into the matter following talks with the FA, which founded the WSL in 2011.
No timeframe has yet been proposed, with the BBC stating that any takeover could be “several seasons away”, and neither the Premier League nor the FA would comment.
The FA are believed to be open to the idea because they see the women’s England teams and grassroots participation as their long-term priorities.
The WSL is a full-time professional competition with 12 teams for 2019-20 and was recently boosted by a £10 million sponsorship deal with Barclays.
That agreement reflected the rise in popularity of the women’s game.
England’s dramatic women’s World Cup semi-final defeat to the United States this week was the most watched television event of the year so far in the United Kingdom, attracting a peak audience of 11.7 million.
The Lionesses bowed out after missing a late penalty in a 2-1 loss to the world champions.
Viewing figures released by the BBC showed that the match in Lyon grabbed a peak share of the TV audience of over 50 percent.
It was the fourth time this tournament that the record UK TV audience for a women’s match had been broken.