Falkirk have been told to produce further proof that they can satisfy rules for entry to the Scottish Premier League.
Falkirk's delegation arrived at Hampden in high spirits
SPL chairmen remain to be convinced that the First Division champions' fixtures will take precedence over present tenants Airdrie United at the Excelsior Stadium.
But Falkirk chairman Campbell Christie will have been heartened by the response to the ground-sharing proposal with the Second Division club that he hopes will be enough to win his club promotion.
SPL chairmen will vote on 23 May on whether to allow Falkirk entry to Scotland's top tier.
But, following Thursday's meeting at Hampden, Dunfermline Athletic chairman John Yorkston said: "From my own point of view, if they got confirmation that they had tenure for next season, that would satisfy me."
We have agreed to clarify a particular aspect of our leasing agreement
Falkirk chairman Campbell Christie
That will please Falkirk following reports suggesting that they will struggle to win the 7-5 majority required.
Christie said: "We have agreed to clarify a particular aspect of the back-up arrangement to our leasing agreement for Excelsior Stadium and we are confident that this can be done to the SPL's satisfaction.
"We have a clear-cut agreement with Dudley Developments Ltd, the preferred buyer of the Excelsior Stadium, that provides us with priority access to the ground for all SPL fixtures, Scottish Cup and CIS Cup ties.
"We understand that the sale agreement is expected to be concluded very soon and we believe the fall-back arrangement will not be called on.
"However, in the light of newspaper comments attributed to a local councillor, some clarification is required about a formal back-up agreement with KPMG, the liquidators of Airdrieonians FC and North Lanarkshire Council, in the unlikely event of Dudley not acquiring the stadium."
The former leader of North Lanarkshire Council, which owns Excelsior Stadium, known also as New Broomfield, suggesting that Airdrie United would be given priority.
But council head of property services Ian Nisbet said: "First and foremost, it has always been North Lanarkshire Council's priority to secure the provision of a senior football team for Airdrie in the sale of the New Broomfield Stadium, along with the redevelopment of the Craigneuk pitches.
"Beyond this, the future use of the New Broomfield Stadium is a matter for the potential owners and Airdrie United.
"North Lanarkshire Council, which is very much a third party in this situation, is aware that a number of negotiations have taken place, and are still ongoing, between KPMG, Airdrie United, Falkirk FC and the potential owners.
"These negotiations are well advanced and the council has endorsed a provisional agreement with regard to possible ground-sharing.
"This has still to be formally concluded and will not compromise our commitment to Airdrie United."