Ten clubs have written to the SPL proposing the formation of an SPL2 after becoming frustrated with the lack of progress over league reconstruction.
However, Scottish Football League chief executive David Longmuir has warned the rebel clubs that there will be no appetite for their entry among top-flight clubs.
Hamilton chairman Les Gray revealed clubs had been disappointed by the response of Longmuir following the failure to secure a merged league with wealth redistribution measures.
That plan was vetoed by St Mirren and Ross County at an SPL meeting last month on the grounds they did not agree with the proposed split of the top two divisions.
Both those clubs are understood to favour some form of play-offs between the top two flights, ideas for which will be discussed at an SPL meeting on Tuesday, although there is no guarantee enough of the remaining 10 clubs will back the plans.
The clubs will also discuss the fresh proposal and Gray believes it can work.
He told BBC Radio Scotland: "I have spoken to the SPL chairmen and I have always felt there was some warmth towards the idea of a second tier, but it has never got over the line.
"We are going at it from the angle that this is the last chance to do something for next season and there is a will to do it. There are clubs in danger, there are clubs having to consider part-time, and there are jobs in danger. We need to try to get this through so that we can create extra wealth for that second tier."
The SPL confirmed they would discuss the proposal.
- Sports & Recreation