"US Soccer definitely believes that the best way forward for everyone involved and for the future of American sports - a single replacement structure for both senior national teams," the association wrote in a statement.
The association also wants the ladies' and men's player unions together with the association to work for equal compensation to the national teams from the World Cup tournaments.
"US Soccer will not agree to compensation agreements if it does not take the important step of making the World Cup prize money equal," said the US Football Association.
The ladies of the United States are the reigning world champions and took bronze in the Olympics in Tokyo.