FAW chief executive Jonathan Ford believes the joint proposal would be “strong and compelling”.
The Scottish FA has also confirmed that exploratory discussions have begun, while the FA is already looking at a bid that Uefa has previously said it would “strongly support”.
Ford confirmed there is set to be a feasibility study into the prospect.
A Downing Street spokesman has also said the UK government would be supportive of a bid involving the home nations.
The SFA says its current focus is on Euro 2020, with Glasgow one of the host cities for the tournament, but BBC Scotland understands the Scottish government is aware of the discussions and would also support any bid.
“This is something that has come up in conversation and it is something we are looking into,” Ford told BBC Sport Wales.
It came after Fifa vice-president David Gill said England should have “great confidence” in bidding for the 2030 tournament, having lost out to Russia for the right to host the 2018 tournament.
An SFA spokesman said in July it would be “open-minded” about a joint bid while, earlier this month, Northern Ireland manager Michael O’Neill said hosting World Cup games at Windsor Park would be “huge” for the country.
Argentina, Uruguay and Paraguay have announced their plans to jointly bid for 2030 while Tunisia would be open to the idea of a North African bid along with Algeria and Morocco.
“The reality is for countries like Scotland, Wales, Northern Ireland, it’s always going to be a case of having to do it in partnership with another, and the logical partner for us would be England,” added Ford.
“You need a lot of stadia now; of course, the structure of the competition has changed - you need 16 40,000-seater stadia.
“Of course, we have a fantastic stadium with the Principality Stadium and we’d love to be there, but there’s a lot of discussions to be had.”
Asked whether the potential bid would include all four home nations, Ford said: “All of the discussions are still being had, so there’s a lot of wait and see.”