Edinburgh Rugby are investigating the redevelopment of Meadowbank Stadium as a 10,000-plus capacity stadium that could also be used by the city's two senior football clubs.
Meadowbank Stadium presently has only one stand
Hearts and Hibernian are already in the process of consulting fans about a proposed joint venue at a greenfield site in Straiton on the outskirts of Scotland's capital.
But Hibs have admitted that selling their present Easter Road ground and moving the short distance to the former Commonwealth Games venue is another option they would consider.
And Edinburgh chief executive Jim McKenzie told BBC Sport that they have a working group established with funding body Sportscotland about redeveloping their present home ground.
Edinburgh have been examining other sites in the city - including Meggetland, which Boroughmuir are themselves planning to redevelop - but Meadowbank is their preferred option.
McKenzie said: "If the two football clubs decide to groundshare, it might provide another opportunity for us."
Edinburgh and Sportscotland are presently investigating new stands at both sides of the pitch but could expand that with stands at each end should the football clubs become involved.
Hearts might be less ameniable to such a plan as their fans are unlikely to welcome a move to the traditionally Hibs-supporting east of the city.
However, Hibs fans have been less enthusiastic about the move to Straiton and a move to Meadowbank could prove to be a more acceptable compromise.
The club's board see the sale of Easter Road as a way of reducing crippling debts.
Hearts must move from their Tynecastle Stadium as the pitch does not comply with Uefa regulations.
Edinburgh Council are also investigating the future of Meadowbank and athletics in the city.