Representatives from the 12 clubs discussed plans for a 10-team top flight in a three-hour meeting, which was originally earmarked as a chance to vote on SPL chief executive Neil Doncaster's draft plan.
The Aberdeen chairman said: "I think it is still moving in the right direction. There is a bit of work to do. I think there will be a vote some time in the middle of May."
Hamilton chairman Ronnie MacDonald and Dundee United counterpart Stephen Thompson declined to comment in detail after emerging from the meeting, with the SPL board due to release a statement later.
But Thompson felt some progress had been made and Milne is optimistic that can be built upon in the coming weeks.
When asked if the clubs were still on track for a reduced top division, Milne said: "I think we're on course to go somewhere. It's still very much the plan that is on the table."
However, Kilmarnock chairman Michael Johnston was far less optimistic over the likelihood of consensus emerging soon.
"I think we are just where we were when the meeting started," said Johnston, a firm opponent of a smaller league. "There are people strongly in favour, there are people strongly against.
"There are a number of people sitting in the middle. In some meetings they seem to be more in favour, other meetings they are more against the proposals.
"But I think the bottom line is there is still work to be done before we reach a situation where everybody is going to agree that there is a plan for the way forward. And there are some fundamental issues which I have, which need to be addressed."
Source: PA
Source: PA