Councillor Andrew Burns, leader of the Labour group on the city council, had called for the report after noting the one-year anniversary of the start of the dispute.
Most of the groups who were involved in the disagreement – including street cleaners and grave diggers – have agreed to return to normal work. But a deal has not yet been agreed with bin men, who remain on a work-to-rule.
Council leader Jenny Dawe said: "Once the dispute is settled, we will be able to produce a figure.
"Most of the groups who have been in dispute have now returned to normal working, which vindicates our stance in keeping on negotiating and trying to get people back to work."
The council has previously said that the gross cost of the dispute was 5.4 million up to March.