Chelsea Ladies' won the 2018 FA Cup final in front of a record crowd of 45,423 at Wembley.
The Football Association has submitted a bid to host the Women's European Championship in 2021.
England hosted Euro 2005 and reached the 1984 and 2009 European finals.
FA head of women's football Baroness Campbell told BBC Sport: "It would be enormous to have a major championship like this on home soil.
"Uefa will want a bigger and better tournament than the last one and we've got Wembley as a key card to play, to host the final."
Women's football in England has grown since it turned semi-professional with the start of the Women's Super League seven years ago, with attendances in the domestic game peaking at an average of 1,128 after England finished third at the 2015 World Cup.
Last season, there was a record Wembley crowd of 45,423 at the FA Cup final but WSL crowds dipped, coinciding with a move back to a winter league after six years of summer fixtures.
In January, the FA announced an additional £50m of investment in women's and girl's football over the next six seasons, taking the total investment from the 2018-19 season onwards to £114m.
A positive showing under England boss Phil Neville at the 2019 World Cup in France would also help boost the game's popularity.
Neville's side are fourth in Fifa's rankings behind the United States, Germany and France, who they beat at the last Euros for the first time in 43 years.
Source: bbc.com