The Paisley chief joined with Ross County chairman Roy MacGregor to vote down Scottish Premier League plans for a new 12-12-18 set-up on Monday. That led to online rumours that Gilmour had acted on behalf of the Ibrox club after welcoming their chief executive Charles Green to St Mirren Park for the Buddies' clash with Celtic last month.
Aberdeen chairman Stewart Milne, meanwhile, suggested Gilmour had an "agenda" behind his decision to vote against the proposals, while Hearts chief executive David Southern suggested St Mirren concerns on voting structures were a "smokescreen to protect other people's interests".
But Gilmour told Press Association Sport: "These rumours sound like a conspiracy theory. Any club official who would suggest such a thing, we would look at it legally because it is absolutely slanderous. The St Mirren board are only interested in what is in the best interests of St Mirren Football Club and that will always be the case."
Had the plans for the new league structure gone through, Rangers would have remained in the basement league, despite winning the Irn-Bru Third Division with five games to spare.
But with talks on reconstruction having now seemingly hit the buffers, the fallen Glasgow giants will instead be promoted to the third-tier Second Division.
Gilmour - who, along with fellow boardroom members, persuade Saints shareholders to axe club director Ken McGeoch following revelations about alleged links to former Rangers owner Craig Whyte - however, insisted he was looking out for all of Scotland's senior clubs when he voted against the plans over concerns about fan backing for the new set-up and the 11-1 voting structure.
Asked about the Rangers rumours, he said: "It's ridiculous. This is a club that voted Rangers into Division Three, voted a director off our board because of alleged links to Rangers.
"We are also a supporter of a 42-team solution for Scottish football, not an SPL2, and that would therefore have no short-cut for Rangers back to the top-flight, so where somebody would get the idea that we were doing this to help Rangers is beyond me."
The Scottish Football League were due to poll their 29 full-member clubs on Friday, had the SPL reached its required 11-1 majority in favour of change. But with the 10-2 result following St Mirren and Ross County's no votes, the SFL will no longer hold their own ballot.