The East of Scotland League club are preparing their application in the expectation that Gretna go under next week.
Spartans, who took St Mirren to a replay in last year's Scottish Cup, appear to be favourites but Annan Athletic, Preston Athletic and Cove Rangers are also in the frame.
The clubs were alerted on Thursday when SFL members voted to demote Gretna to the Third Division following their relegation from the top flight.
Gretna, whose employees were all made redundant by administrators, are expected to be wound up next week after SFL chief executive David Longmuir found "fundamental flaws" in the business plan put forward by the sole interested party.
Spartans general manager Derick Rodier revealed the north Edinburgh club were preparing their application.
"The preparations are tentative but nevertheless we are looking at various things," he said.
"We are moving into our new Ainslie Park stadium in the summer and the pitch will be ready for the end of August.
"Our long-term aim was always to get in to the SFL but we are not counting any chickens."
East of Scotland League rivals Annan have notified the league of their interest in replacing neighbours Gretna.
Club secretary Alan Irving said: "We have a new 500-seater stand and concrete terracing right round the ground.
"The only stumbling block might be the floodlights. We have planning permission to erect them and we were in the throes of trying to get funding before all this blew up. That was planned to happen this calendar year."
Highland League champions Cove Rangers appear to be the only club from the north preparing a bid.
Cove chairman Keith Moorhouse told the Press and Journal: "Our application would be based on us sharing a purpose-built new community facility, which is already well at the advanced stages of planning, and not on our current Allan Park ground.
"A new stadium would not be ready in time for next season, so obviously we would look for the Scottish league to allow us to play out of our existing ground until the new stadium is completed."
Preston Athletic, who were rejected by the SFL in 2000 and 2002, when Gretna were admitted, also intend to apply.
They have been in discussions with East Lothian Council over moving to a new stadium and forming a club that would capitalise on the county's lack of top-level football.
East of Scotland leaders Whitehill ruled out an application while Edinburgh City are unlikely to apply. Junior football giants Pollok have also ruled out a bid.
