A number of American cities named in the running to host games at the 2031 Women’s World Cup are considering withdrawing over concerns related to Fifa’s handling of this summer’s World Cup.

The Guardian has learned that several cities are exploring whether to focus solely on winning the right to host matches at the men’s 2031 Rugby World Cup. The US will also stage the women’s rugby tournament two years later.

There are 40 stadiums on the US Soccer Federation’s longlist for potential 2031 venues, and World Rugby has expressions of interest from 27 cities featuring 33 stadiums, of which 20 are on both lists.

Chicago and Pittsburgh declined to enter the running for Women’s World Cup hosting rights, understood to be because of concerns about Fifa’s financial demands, and some cities are considering pulling out.

A source working with one of the cities that has held talks with Fifa and World Rugby said the latter was offering far greater commercial freedom and has fewer demands regarding access to stadiums.

Another source at a city committed to bidding for the Rugby World Cup said that event was likely to be more profitable, owing to the demographic profile of rugby supporters and a belief they will spend more money while attending matches.

Fifa last month put back confirmation of the 2031 World Cup hosts from the end of this month to an unspecified date this year, although the joint proposal from the US, Mexico, Costa Rica and Jamaica is the only one on the table.

Fifa explained the delay by saying it planned to stage a one-off extraordinary congress to determine the 2031 and 2035 hosts, as it did when allocating the 2030 and 2034 men’s tournaments.

The Athletic reported that the US government had yet to provide Fifa with mandatory guarantees for 2031 regarding obligations on visas, tax, safety and security, ordinarily granted by the host country before the bidding process is complete.

As the primary host federation, US Soccer last year highlighted 14 US stadiums as preferred venues on a 20-strong shortlist for the 48-team tournament, with a further 26 stadiums endorsed as potential venues.

Seven of those 40 stadiums are hosting matches at this summer’s men’s World Cup, and their experience of dealing with Fifa has not been uniformly positive.

Fifa has insisted the host cities bear the costs of safety and security around stadiums this summer, but it is keeping income from broadcasting, sponsorship and ticket sales, which has led to tensions.

A long-running standoff over who would pay for security at the Gillette Stadium in Foxborough, Massachusetts, was resolved only last month. Gillette Stadium is in the mix for both tournaments in 2031.

There remain problems – some related to Fifa – over public transport at many venues, and several cities have cancelled official Fan Fests or reduced the number of days they will be open. They were meant to operate in every city throughout the 39-day tournament.

World Rugby announced its stadium shortlist before a New Zealand v Ireland match in Chicago last November, which attracted a sellout crowd of more than 61,000 to Soldier Field.

That list will be reduced to between 10 and 15 stadiums via a tender process, which is likely to lead to some cities choosing which World Cup to bid for.

World Rugby has made clear it will finance its event and share profits or losses with USA Rugby, rather than requiring the hosts to underwrite the tournament.

In an attempt to attract bids from NFL stadiums World Rugby has reduced the exclusive access windows in which it requires control of the venues, because the tournament will clash with the 2031-32 American football season.

The US Soccer chief executive, JT Batson, told the Guardian that the federation had “incredible demand to host in 2031”.

Fifa declined to comment beyond referring to a statement on the 2031 and 2035 World Cup bidding processes last month: “Fifa will convene an extraordinary congress before the end of 2026. This extraordinary congress will be a standalone event dedicated to the presentation of the bids, which will highlight the growing power and influence of women’s football and Fifa’s flagship women’s tournament.”

World Rugby declined to comment.