Representatives from the 12 clubs are attending a 10am meeting at which major reform proposals are very much in the balance given two clubs could veto the plans.
St Mirren have already confirmed their intention to reject the plans, which include a merged 12-12-18 set-up with extended play-offs, a more equitable financial distribution and a pyramid structure.
The Paisley club do not like the league structure, which would see the top two divisions split into three after 22 games, and have reservations over the retention of the 11-1 voting system on some protected issues for three years.
And Gilmour said: "I don't know until we get in there but I hope we can have some form of compromise.
"One must stand with what one thinks and feels with one's heart and one's head. However, I do think there's a way forward to get into one body; way forward for an all-through distribution model and I'd like to work hard towards that."
Gilmour added: "Why should we not cherry-pick? Take the good points and get the good points moving. I think that's the way forward for Scottish football."
However, Milne felt such an approach was overly-idealistic given the compromises already struck to reach the point where SPL clubs agreed in principle in January.
"That's a very easy thing for people on the outside to say," the Aberdeen chairman said.
"If you had any idea of the compromises we went through to get to the stage where there's one plan on the table, you would understand why you can't put all this effort and compromise in, then want to pick out the bits we don't like and discard them. It's fixed up as a plan, a whole plan. It doesn't stack up if you start to pick out the bits you don't like."