"Whether we follow it up with a full application, I don't know, but it would be a shame if we were to miss the boat," said Clayton.
"We certainly don't want to rule ourselves out at this stage."
Gala, whose most famous product is former Celtic and Everton midfielder John Collins, have had a lean period in the East league in recent seasons and finished fifth in Division One this term.
Spartans, who are the bookmakers' favourites to replace Gretna, finished third in the Premier Division, with fellow applicants Preston in fifth and Annan in seventh.
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