Jeremy Purvis, the Lib Dem finance spokesman, who is set to meet finance secretary John Swinney this week to thrash out an agreement, signalled that compromise was on the cards.

In addition, the two Green MSPs, whose support would be vital, have indicated they are now ready to talk about the policy. Although there were talks before the summer, the SNP and Lib Dems have been split – the SNP wants a centrally set rate of 3p, but the Lib Dems want local councils to decide the rate.

Speaking to The Scotsman, Mr Purvis made it clear his party could strike a deal on the major sticking-point and give councils control of tax rates after a bedding-in period.

If this happens, the SNP would only need to find support from the Greens – though if the SNP wins the by-election which would be called if the former first minister, Labour MSP Jack McConnell, becomes High Commissioner of Malawi, they would only need independent MSP Margo MacDonald's vote in Holyrood to carry their plans.

The Greens, who favour a land value tax, said yesterday that they could be flexible. A spokesman said: "We are open to discussion on this issue because there is no doubt the council tax needs replacing, which is the weakness of most parties opposed to LIT. We want a land value tax, but if we can get that into the mixture of options for councils … then there is a room for agreement."

Ms MacDonald said she would back LIT if it can be operated at no great cost and she could have guarantees it will be fairer for the majority of Scots. She said: "There are some big questions to answer, but I can be persuaded if Mr Swinney can reassure me on those points and show me that only a small number of wealthy people can avoid it."

The political breakthrough came despite evidence that support for LIT is tumbling – a new poll put public backing for it at 46 per cent, just 15 per cent above the council tax, compared to 88 per cent support a year ago. The SNP has insisted this figure was reached after the "don't knows" were taken out.

Senior figures in the Nationalist parliamentary group have suggested the centrally set rate could be in place for the first few years before Scotland's 32 councils were allowed to set their own rates, once the system was bedded in.

Mr Purvis said this would be an acceptable solution. "Obviously any new tax system would take a year or two to bed in, so it would be completely reasonable to have a centrally set rate in that transition period and then allow councils to set their own rates," he said.

"I'll be meeting with John Swinney this week and if that is what he has to offer and it's not just something being aired by SNP MSPs, I think we can find a solution. There is a big difference between having local accountability introduced over time and not having it at all, which is the current proposal.

"The sticking point for us is local accountability and the ability of councils to raise their own taxes. If that can be overcome, then we can move forward."

The Lib Dem solution, which potentially would see businesses having to pay 32 different rates, is the nightmare scenario outlined by the Institute of Directors, CBI Scotland and Federation of Small Businesses. In their submissions to the consultation on LIT, they warned that it would create administrative chaos and overburden businesses with paperwork.

But Mr Purvis insisted LIT was not as expensive and complex as critics were claiming: "Essentially it is quite simple, you simply set the income tax rate to the person's postcode, which is a lot cheaper and simpler than going through valuations of property."

But there has been stinging criticism from Labour, who still believe there needs to be a property-based tax.

Cathy Jamieson, the acting leader of Scottish Labour, said: "It looks like we are likely to have a dodgy back-room deal between the SNP and Lib Dems, as we warned. The Lib Dem plans are even worse than the SNP's, which is difficult. This is simply a recipe for chaos."

A Scottish Government spokesman said it was open to informal talks with various parties, but was currently sticking to the original proposal of a 3p centrally set rate. As well as business groups, LIT is also opposed by the Institute of Chartered Accountants, Unison, the National Union of Students, Glasgow City and South Lanarkshire councils, the STUC, Carers Scotland, the Society of Local Authority Chief Executives, local authority finance officers, the Policy Institute, the Treasury and range of experts.

They have questioned its fairness, legality and cost and warned that the wealthy with non-salary incomes will be able to avoid paying it.