Andrea Bradley, general secretary of the EIS, said it stands ready to consider a new offer “as soon as it comes to us at the beginning of the working week”.
The union rejected a five per cent pay increase in September and its members are set to walk out on Thursday.
It will be the first national strike action over pay for almost 40 years, with nearly all schools expected to close. Two further strike dates have been announced on January 10 and 11.
It comes amid a wave of planned strike action, with paramedics, train drivers, university staff and postal workers all set to walk out in the coming days.
Deputy First Minister John Swinney previously made clear to unions that finding extra cash to fund public sector pay rises beyond what has been offered would mean more cuts to services.
Mr Swinney said: “If I want to put any more money into a public sector pay deal, beyond what’s already on the table, I have to cut public expenditure and public services.”
Speaking yesterday, Ms Bradley said: "As things stand, the EIS continues to plan for a day of national strike action on Thursday, which is likely to close almost all schools in Scotland.
"We are hopeful, however, that over the course of this weekend, Scottish Government colleagues and [council umbrella body] Cosla colleagues will have been able to arrive at an agreement around a more substantial offer than the five per cent that was rejected in the middle of September."
She added: "We are ready to consider a new offer as soon as it comes to us at the beginning of the working week."
Ms Bradley said she is "very hopeful" of a new offer, adding: "I've been in informal discussions with the Scottish Government and I am hopeful that something that will be worth considering by our salaries committee will be forthcoming at the beginning of the week, and with that in mind, we’ve scheduled a special meeting of our salaries committee to take place on Tuesday and a special meeting of our executive committee to take place on Wednesday. So we are more than ready to consider any offer that comes forward from the Scottish Government and Cosla over the course of the next couple of days."
The EIS has been pushing for a pay rise of 10 per cent, citing the impact of soaring inflation.
Ms Bradley called for "proper investment" in education, adding: "Our argument is that when you underfund education it is ultimately the children and young people who the education service is supposed to benefit who will be disadvantaged."
She said the EIS has been in discussions with the Government since "before April this year".
She added: "Teachers should have had a pay increase in their bank accounts on April 1. This is now the middle of November and they have had nothing, zero, by way of a pay award against a backdrop of rising inflation, which means that they are struggling, they are struggling to meet the cost of food, fuel, energy, housing, such that some of our own members are now visiting foodbanks.”
Ms Bradley described discussions with the Scottish Government as "constructive to a point", insisting ministers knew "well in advance that there was going to be a substantial teacher pay claim coming this year". She added: "They knew it when the 2.2 per cent was reluctantly accepted last year. They knew to expect this, and yet they haven't planned adequately for it, so the responsibility for that rests with the Scottish Government."
Scottish Conservative education spokesman Stephen Kerr said SNP Education Secretary Shirley-Anne Somerville “has been AWOL as the threat of teachers going on strike has loomed large in recent months”.
He said: “The SNP Government have sat on their hands despite knowing substantial pay claims were coming this year no matter what. Teachers are clearly sending out a message that the SNP have failed to prepare, and now they are preparing to fail as strikes will shut nearly every school in Scotland on Thursday.
“Our young pupils suffered enough disruption during the pandemic and missing out on more classroom time is the last thing they need. The buck for this imminent strike action stops with the SNP Government.
“They claim education is their top priority but have failed to address these threats with any sort of urgency. There is still time for Shirley-Anne Somerville to show some leadership, get back round the table with the unions, and avoid the school gates being closed this week which will cause huge disruption across the country.”
Scottish Liberal Democrat education spokesman Willie Rennie said pupils faced enormous disruption during the pandemic and the last thing they needed was “more upheaval caused by these strikes”.
He said: “There is no doubt that these strikes will be hugely disruptive but teachers can only be pushed so far. The blame for all of this can be traced back to the SNP's invisible Education Secretary. Teachers have seen class sizes soar and classroom support plummet.”
He added: “Now that the Scottish Government have seen details of the UK Government's budget, there can be no more excuses for delays. A pay deal needs to be reached in the next few days. If these strikes go ahead she will owe parents, teachers and pupils a public apology.”
Ms Somerville said: “We are absolutely committed to supporting a fair pay offer for teachers through the Scottish Negotiating Committee for Teachers, the body that negotiates their pay and conditions of service.
“I spoke to trades union representatives on Friday and restated that I am keen to work with Cosla, as the employers, to allow them to make a revised pay offer and avoid unnecessary strikes.
“I have been clear, however, that the Scottish Government has a fixed budget and if we are looking to fund public sector pay offers, then that money must come from somewhere else in the budget.”