The offer of talks follows a decision by the heads' unions to make public their frustration and anger at the "total confusion" in the authority's budget strategy.
While deploring their high-profile approach, Jan Wilson, the new chair of education, is willing to see what improvements can be made.
According to the National Association of Head Teachers and the Secondary Heads Association, schools lack confidence in the council's leadership, its planning and its delivery of funding.
As a result of four years of financial crisis, heads say they are unable to fulfil their statutory obli-gations relating to the national curriculum, health and safety, school security and special needs.
The unions claim Sheffield retains nearly Pounds 17 million of its education budget (Pounds 3.5m above the national average), to the detriment of individual schools.
They also accuse the authority of "lurching from one crisis to another", with gross errors in the 1996-97 budgets leaving schools unable to plan expenditure.
Even allowing for a tight spending assessment from central government, Sheffield spent only Pounds 2,159 on each secondary school pupil, compared with Pounds 2,500 in Manchester and Pounds 2,300 in Liverpool, the unions add.
Speaking at a joint press conference in Sheffield, NAHT general secretary David Hart said: "Clearly there is something wrong in the state of Sheffield that it should be so much out of kilter with other metropolitan authorities. . . . Not only is Sheffield holding back more than the national average, but the position has worsened this year."
Heads are calling on the city to reduce its level of hold-back to the national average of 10 per cent - a figure that is also in line with Labour policy nationally.
They also want spending to increase over the next three years to match the national average for primary and secondary schools. And, they say, the city must develop a "genuine partnership" with heads in which their legal responsibilities are recognised.
Graham Elliott, a secondary school head and SHA convenor, told the meeting: "There is a question about the honesty of information about why we are in a particular situation."
As an example of the department's inefficiency, he told how an arson attack at Christmas dam-aged his school's water supply. After months of repairs, which caused huge disruption, his financial plans were thrown into disarray by a Pounds 17,000 bill for the work, which he was now disputing with the council.
Jan Wilson rejects much of the unions' argument. She says Sheffield increased its spending on education last year, at a time when other departmental budgets were cut.
She points out that money spent centrally is not "extra" - if it were devolved to schools, the costs would be too. But she added: "We are always hoping to improve. It is very important that we work together."
The post of director of education, vacant since December, is to be advertised, possibly at a higher salary.