According to a spokesman for Mr Saatchi: "There have been several attempts to come to an agreement, and these will continue right up to the very end."
The two sides are due in court early next month to settle charges of breach of contract against three former Saatchi & Saatchi executives, David Kershaw, Jeremy Sinclair and Bill Muirhead. They have signalled that they will join a rival firm established by Mr Saatchi following his ouster from Cordiant late last year.
Maurice Saatchi and his brother Charles are also being sued. Cordiant has withheld bonuses from the executives until a settlement is reached.
"There's no doubt it is in the best interests of both sides to secure a settlement," the spokesman said. "Neither side wants this to drag out just to make the lawyers rich."
He added: "No judge is going to say [the three executives] have to wait up to three years before they join a competing agency. But then again, nor will a judge dismiss the contractual obligations."
Until the legal issues are resolved, the three defectors are able to take only "preparatory steps" towards joining the new agency.
Since the beginning of the year, New Saatchi, as the rival is temporarily called, has wrested several high-profile accounts away from Cordiant, most recently British Airways.
Insiders at Cordiant believe the damage is now done, and want an end to the adverse publicity.
Any settlement would be likely to include clauses preventing New Saatchi from soliciting business from Cordiant clients or poaching Cordiant staff.
Several Cordiant account executives have already joined New Saatchi, which now has about 80 staff in place. They are working on three accounts - Mirror Group, Gallaher, the maker of Silk Cut cigarettes, and Dixons, the high street electronics retailer - that New Saatchi took from Cordiant since the beginning of the year.
Meanwhile, no formal suit has yet been launched by Cordiant to share in the proceeds of a controversial stock-option deal involving Adidas, the footwear manufacturer. It is believed the transaction could be worth $40m. Cordiant argues it is a reward for work done for the agency and does not belong to the Saatchi brothers.