Longmuir claims "anything is possible" but insists the 30 clubs in his set-up and 12 in the Clydesdale Bank Premier League must first agree over the controversial matter of timescale.
Third Division leaders Rangers have voiced their anger at suggestions a new league structure could be hurried through in time for next season, claiming their current campaign would be rendered meaningless if reconstruction means they will still be playing in the bottom tier of a new set-up.
Opinion on the matter was split as the SFL held its first round-table talks with all 30 of its members at Hampden.
Representatives from several sides voiced differing views on the matter as they arrived for the meeting in Glasgow's south side but they did agree to push forward with proposals for either a 12-12-18 set-up or an alternative involving two bottom leagues made up of 10 teams each.
Longmuir, though, claims if consensus eventually points to a desire for an early start, it could yet happen.
He told Press Association Sport: "Any change is deliverable if there's a will and a consensus to go for it.
"We want to see improvement in the game and that is ultimately all our aim here. The quicker we can bring that about the better. Whether it's achievable or not for next year is another matter and that will be determined by what we can do over the next few weeks and months in terms of bringing the rules together.
"The board will get together over the next couple of weeks and see where we can take it.
"We will start the work now behind the scenes to take a look at the detail."
- Sports & Recreation
- Clydesdale Bank Premier League