First Minister Alex Salmond will attempt to secure vital votes for the Scottish budget when he meets Labour leader Iain Gray.
A deal to pass the Scottish budget on the second attempt is imminent, it has emerged.
The talks are expected to centre on funding for apprenticeships.
The minority Holyrood government has been trying to win support for the £33bn spending plans for 2009-10, which parliament rejected last week.
It is believed the budget could be fast-tracked through parliament on Wednesday - one week after the first version was thrown out.
It is understood a deal has been reached with the Liberal Democrats.
Labour, the Liberal Democrats and the Greens had combined to vote down the £33bn spending plans.
Their support - combined with the votes of the Conservatives, who supported the bill last week - would give the SNP the majority it needs to pass the budget.
A spokesman for Mr Salmond said a number of "productive meetings" - including one with Green Party leader Patrick Harvie - had taken place since last week's vote.
It is also thought Labour will be offered less than their current demands on boosting apprenticeships.
On Monday, Finance Secretary John Swinney held talks with Liberal Democrat finance spokesman Jeremy Purvis. The first minister is due to have discussions with Mr Gray on Tuesday morning.
Labour, the Liberal Democrats and the Greens combined to vote down the budget in parliament last week, saying it would fail to help the Scottish economy through the current tough times.
Labour has already offered to back the budget in return for a scaled-down concession on apprenticeships.
However, it is now understood that the Lib Dems will back the budget in return for two long-term economic aims.
Agreement hopes
Ministers have agreed to press the Calman Commission, which is reviewing devolution 10 years on, to agree to borrowing powers for Holyrood.
The party had originally sought, and was refused, a budget commitment to providing an extra 7,800 apprenticeships a year for each of the next three years.
And there will be a cross-party review of Scottish Government spending.
But Mr Gray said last week that his party would now accept a commitment to introduce 7,800 apprenticeships for each of the next two years with an "indication" that this would continue for a third year - a proposal which would cost between £45m and £90m over three years.
Ministers are also working on plans to fast-track the Budget Bill through parliament.
Speaking ahead of the meeting, Mr Gray said: "I hope we can reach agreement.
"Most Scots recognise that our call for an increase in apprenticeships is not just reasonable, but something the Scottish Government should do now.
"It just cannot be right that a young person in England has more than twice the chance of getting an apprenticeship than their equivalent in Scotland, and we cannot accept it."
He added that his party had scaled back its demands on apprenticeships, but added: "We feel it is right to offer that compromise to provide young Scots with the best chance possible at a time like this."
