England may bid for future men's and women's international tournaments with Gianni Infantino now leading Fifa, says Football Association boss Greg Dyke.
The FA backed Infantino in Friday's Fifa election, in which he polled 115 votes to succeed Sepp Blatter.
Dyke told the BBC's Sportsweek the FA had not bid for recent tournaments because they "did not trust the system" in place at Fifa under Blatter.
But he added: "I do think if the opportunity comes up we should bid."
He continued: "If we think it is a fair system and England wants to bid - for men's or women's tournaments - we should bid.
"There are a couple of men's tournaments coming up, which are the men's European Championship in 2028 and the World Cup in 2030.
"I don't suppose you can have both so we would have to decide which one to bid for. And as long as it is done openly and fairly, unlike what happened last time, we would have to decide as a country if we want to go for it."
England lost out to Russia in bidding for the 2018 World Cup.
In October last year, Blatter suggested there had been an agreement in place for Russia to host the event - before the vote took place.
The bidding process for the 2018 and 2022 tournaments is the subject of an ongoing Swiss criminal investigation, which began alongside a US inquiry following the arrest and indictment of several top Fifa executives by the US Department of Justice on corruption charges.
As well as appointing a new president on Friday, Fifa also passed key reforms to help make it a more transparent and accountable organisation.
A senior Fifa source said Infantino will be paid less than the soon-to-be-appointed chief executive, and neither will get as much as Blatter, who was paid around £4m a year according to some reports, which have not been denied by Fifa.
Blatter quit in May amid allegations that led to a six-year ban from football, which he is contesting.
A Fifa source said that while all payments to Blatter had ceased, he is being allowed to keep his company Mercedes until his appeal process is complete. Blatter is also renting a Zurich apartment from Fifa on commercial rates.
His resignation prompted the extraordinary congress at Fifa, which has been engulfed by claims of widespread corruption since summer 2015.
Dyke was pleased at the result of the election, where lawyer Infantino secured 27 more votes than closest rival Sheikh Salman bin Ebrahim al-Khalifa.
"[Infantino is] very competent, very organised, very together. Not a showman, but good fun. He has got a lot of qualities and it will be very good for Fifa," he said.
"It's been a corrupted organisation for a very long period of time. There's a big job to be done. But at least we've got a reform programme and at least we've got a president in whom we can trust.
"The reason we wouldn't deal with a Blatter Fifa is because we didn't think we'd win. And there was so much bad blood from the last time we tried - at government level as well as at the FA level.
"It was almost impossible to deal with him."
Any future plans for England to bid for future tournaments will be dealt with by a future FA chairman as Dyke leaves the association this summer.