Councils later expect to know if they will get more money from the Scottish Government to offer teachers a new salary.
Unions have said any new offer would have to be “significantly” improved to avoid further strikes.
Teachers have asked for a 10% increase, but the current deal is worth between 5% and 6.85% for most staff.
Deputy First Minister John Swinney said discussions on the teachers dispute would continue on Monday.
He did not confirm that a new offer would be made.
A series of teachers’ strikes have been taking place across Scotland since November, with more planned for later this month.
If additional funds are made available by the Scottish Government, a meeting will be held later this week to agree a new agreement before it is put to unions.
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At the heart of the dispute is the pay rise that teachers were supposed to receive in April last year.
The latest salary offer came ahead of the EIS union’s first strike in November.
Almost all pupils in Scotland have lost three or four days of classes since then.
The next strike action is scheduled for February 28th and March 1st.
The EIS is also planning targeted strikes at schools in a number of areas – including First Minister Nicola Sturgeon’s Glasgow constituency.
Cllr Stephen McCabe, leader of Inverclyde Council, told BBC Radio’s Good Morning Scotland he was “on standby” to attend a meeting of the country’s 32 local authority leaders on Tuesday to approve a revised salary offer.
He added: “I don’t know what that offer will look like as I’m not privy to the discussions that are taking place in government.
“I would hope we could find a way to at least suspend the strikes, perhaps pending further discussion of a two-year deal, but at this point I really don’t know what the government will come up with. “
Education Secretary Shirley-Anne Somerville previously said the government was committed to settling the dispute as soon as possible.
She said the government is “pushing forward work on an improved offer for the teaching unions”.
Deputy First Minister John Swinney later told Radio Scotland that “continued discussions” regarding the doctrine dispute would take place throughout Monday.
Mr Swinney said the budget for local authorities had been increased by more than £570m but added he did not underestimate the extent of the difficulties local authorities were facing due to “raging inflation”.
He said: “In a really tight financial situation, the government has significantly increased the resources available to local government.”
Mr Swinney stressed that the Council’s cuts should not affect the number of teachers.
“I struggle to see how we can close the poverty-related education gap without maintaining teacher numbers in our schools,” he added. “Teachers are vital in this effort.”
Mr Swinney also said he could not have gone any further on increasing income tax after announcing in December that anyone earning more than £43,662 in Scotland would have to pay more.
He told Good Morning Scotland: “Anyone who says I haven’t exhausted my options is not properly analyzing what I’ve done.”
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