England will bid for the women’s 2021 European Championship in the wake of the most successful ever tournament in the Netherlands this summer.

The Football Association chief executive, Martin Glenn, said he hoped the bid would lead to a Wembley final, with group games played at Premier League grounds. “We will fill big stadia for women’s games,” he said. “I’m absolutely sure of that. This is an important tournament in its own right and we want to give it prestige.

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“Where we are with the women’s game, this is not an also-ran. We will make it brilliant. It was good in Holland. We’ll take it up a level. I think it would be an absolute win-win, great for the English game but great for the women’s game in Europe.”

Glenn also said he hoped it would be a catalyst for Manchester United to introduce a women’s team. United are the only Premier League team not to have an affiliated women’s team. A fan petition in 2013 urged the executive vice-chairman, Ed Woodward, to follow Manchester City and create a women’s team but it never materialised.

“We think the Women’s Super League is going to continue to attract clubs into it,” Glenn said. “I understand Manchester United, a few years ago, said they might change their minds as the league continues to grow.

“They’re a smart organisation and I think the incentives for competing in the Super League are going to continue to grow. So I think they’ll in time figure out it’s in their interest to do it and this may help.”

A United spokesman said: “We continue to monitor the situation and will make a decision when the time is right.”

One of the FA’s major objectives is to grow girls’ and women’s football in the UK and make it the biggest participation sport in the country for women. Glenn hoped staging a major tournament would chip away at the “nasty prejudice against women’s football”.

“It will be a joyous occasion that will make people feel: ‘Why wouldn’t we play?’” he said, “as opposed to: ‘Why would we?.’”

The final of Euro 2017 was won by the hosts, with more than 27,000 packing the FC Twente stadium. Holland had beaten England in a semi-final watched by a peak audience of four million on Channel 4.

Glenn said that while he would love to bid for a men’s European Championship or World Cup the primary aim of hosting Euro 2021 would be to drive the women’s game. “Half the population are female and they like football,” he added. “Getting them on board is a good commercial thing to do, as well as the right thing to do.”

Talks are continuing between the FA and the Premier League about moving certain FA Cup fixtures from Saturday to midweek but this will not happen until after 2021.

“We are aware that there’s value to the Premier League in getting more games from midweek to a Saturday, there’s value to fans in having that as well,” said Glenn. “There have obviously been discussions around, ‘If the Premier League were to get more Saturdays, what would need to give?’

“If the Premier League wanted more Saturdays and, between us, how can we solve fixture congestion the second half of the season, which is major, then there are discussions about how to do that,” he added. “But they have to be considerate of the value that the FA Cup has to the FA and all the good things that we use the money for.”