Wimbledon and Merton council - the local authority governing the club's natural home area in south London - have been at loggerheads for many years.
The club have accused council leaders of doing nothing to help them move back to their former home, while the council have insisted that it is not their responsibility to help Wimbledon find a new ground.
The threat of the Dons attempting to set up a new home in Dublin - a move opposed by fans in a series of demonstrations at recent games - remains.
But although yesterday's statement contains no specific solution to the problem, the fact that both sides have at least put aside their differences to agree publicly a common goal is a step forward.
Sam Hammam, Wimbledon's owner, has met the new council leader, Mike Brunt, who has been a fan of the club for 20 years, to discuss the possibilities of a new 20,000-capacity stadium on the site of Wimbledon greyhound stadium.
A feasibility study ordered by the council has given this plan the green light, although Wimbledon are understood to want a bigger venue.
However, the two men will be meeting again to discuss "a wider study of the borough to see if we can identify one or more further sites where the club might be acceptably located".
They added: "We fully understand the supporters' anxieties and ambitions, and we give them our word that we are working together to realise their hopes of returning to Merton.
"It is important that the supporters recognise the enormous spirit of goodwill that now exists between us all and trust they will accept that we are doing everything possible to bring Wimbledon home."Reuse content