Canberra's chances of being a host city for the historic tournament will rest with the organising committee, which will be established later this year.

Liberals leader Alistair Coe welcomed Johnson's response, but whether Canberra can host matches will be determined by the cost and government relations are claim and counterclaim about the mooted $1 million per game fee.

The ACT government has also spoken to the FFA, saying it wants to be a part of the tournament as a host city, training base or venue for warm-up games if the parties can agree on the financial commitment.

The Liberals have not said how much they would be willing to pay for games and the use of Canberra Stadium would present another hurdle given it is the only rectangular venue in the city.

The World Cup requires exclusive use of host venues, meaning the ACT Brumbies and Canberra Raiders would have to move away from home for up to three months at the height of their seasons.

ACT Chief Minister Andrew Barr said it would have cost the government $1 million per game to host matches when asked why Canberra withdrew from the bid, describing the fee as "exorbitant".

But a breakdown in communication may have impacted negotiations, with FFA sources adamant there was a cheaper option for Canberra to host three games for a total of $1 million.

The government said it was not informed about the cheaper deal, telling the FFA on September 24 it would not pay a $1 million per-game fee. The FFA's reply, seen by The Canberra Times, did not mention an option to negotiate a cheaper arrangement.

There is still hope, however, with FIFA having the power to change venues or add cities to the host program when the organising committee begins its preparations.

Coe said it was disappointing Canberra was not involved in the initial bid. "The Canberra Liberals believe this is an important investment in women's sport and in our city," Coe said.

Johnson wrote back to Coe, shadow sports minister James Milligan and deputy leader Nicole Lawder, saying: "FFA also shares your disappointment that we were not able to put Canberra forward as a host city for 2023. We would have loved for this to have been the case.

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"... We remain committed to exploring every possibility for Canberra and the ACT to be involved in the FIFA Women's World Cup in 2023 in some capacity."

FFA officials declined to comment on the per-game cost of World Cup matches, but a spokesperson said: "A number of potential investment options were discussed [with the ACT government]."

It's understood part of the FFA's host-city requirements includes costs of security, ASADA doping facilities, venue overlay, public transport, event infrastructure and initial operational costs.

The capital's offer as part of an Australian-only tournament included six to seven matches at a maximum cost of $6.5 million. They would also serve as a base for several international teams, their delegations and fans.

Canberra was then offered three games for $3 million as part of Australia and New Zealand's joint bid, which won FIFA approval last month and sparked celebrations in both countries.

But the the ACT had informed the FFA of their withdrawal last year, more than two months before the final proposal was submitted to FIFA.

The next correspondence was on November 1, when then-FFA boss David Gallop sent a letter to the government acknowledging the withdrawal and saying a "generation of Canberrans" would miss the opportunity.

"It is surprising that the ACT government does not wish to be part of such a global event nor have the opportunity to benefit from this level of exposure to all parts of the world," the letter read.

"It is disappointing that no offer was put forward by the ACT government for FFA to consider whatsoever, even at a level below that which was requested."

Six Canberra training venues - McKellar Park, Greenway Oval, Deakin Stadium, Gungahlin Enclosed, Seiffert Oval and the AIS - formed part of the FFA's submission to FIFA.

It's understood the possibility of hosting more Matildas matches or a pre-World Cup warm-up tournament have been raised as options for Canberra.

The chance to host games would require FIFA intervention, but Milligan is hopeful Johnson's "warm and positive" response changes plans for the capital.

"We know there was a lot of community disappointment at the thought of missing out on this once in a lifetime event," Milligan said.

"As the nation's capital and home to more than 39,000 players, including 7,000 women and girls, we're going to do everything we can to put forward a strong case for Canberra."

The government has invested $20 million for a "home of football" to be built at Throsby. Part of the deal with Capital Football and the FFA was for the Matildas, Socceroos and Young Matildas to play matches in the capital in the coming years.

Johnson said in his letter to the Canberra Liberals the ACT had the highest female football participation rates in Australia, with women making up 27 per cent of the soccer community.