The council is leading a consortium which is looking at the possibility of buying the club to secure its future.
In a statement agreed with club chairman Douglas Craig, Councillor Alan Jones, the council's executive member for leisure and heritage, said today, "We met this morning with chairman Douglas Craig and John Quickfall of Bootham Crescent Holdings to discuss the prospects of a consortium led by the council making a formal bid.
"We were told by Mr Craig that he is currently discussing two serious offers for the club which were likely to exceed any bid from the consortium. The council now wants to discuss with the consortium whether it would be worth making a formal bid at this stage
"In the meantime, Mr Craig undertook to give the council a further assessment of the situation within two weeks. He has also reassured us that all of the parties involved share with us the desire to secure the future of the club."
END