The offer from the brothers' new company, M&C Saatchi, has been turned down by Cordiant, the renamed holding company which still owns the rights to the Saatchi & Saatchi brand, but Mr Saatchi is continuing his efforts to start talks.
Saatchi & Saatchi is the best known name in advertising, although companies seeking an ad agency are unlikely to be confused by the split between the firm and its founders.
The firing of Maurice and subsequent resignation of Charles came last year after a revolt by dissident American institutional shareholders. A six-month moratorium on poaching was agreed last May as part of an out- of-court settlement that saw Cordiant pay the brothers' legal bills.
It came too late to stop the defection of several key employees, and major accounts including BA, Silk Cut, Dixons, Mars and Mirror Group, part-owner of the Independent on Sunday.
M&C Saatchi was expected to start a new spate of client snatching after the agreement expired at the end of last month. The offer to extend the moratorium appears to indicate that the brothers do not have any major targets lined up, said Jennifer Laing, chairman of Saatchi & Saatchi Advertising, Cordiant's UK arm.
"Tim Bell [Maurice Saatchi's public relations adviser] approached me in November about this and there have been several approaches since," said Ms Laing. "He just said the brothers didn't like the M&C Saatchi name and wanted Saatchi & Saatchi back. But it's categorically and absolutely ours and there's no way we would sell it."
Asked to comment on the offer this weekend, Maurice Saatchi would only say: "We're delighted if they continue to use our name. It's free advertising in 50 countries."
Although Saatchi & Saatchi Advertising lost some high-profile clients last year, it claims the total amount of billings that defected to M&C Saatchi was only pounds 90m, and that it has since picked up new business worth close to pounds 93m.
The increase came despite a dramatic cut in pitches to potential clients. Industry sources estimated that it spent about pounds 1m soliciting new business in 1994, but less than a quarter of that amount last year. Hewlett Packard, the US computer maker, is expected to open a new corporate account with Saatchi & Saatchi this month, with billings worth more than pounds 3.5m.
Adam Crozier, joint managing director of Saatchi & Saatchi Advertising, confirmed that the company had been concentrating its efforts on servicing existing clients, resulting in a five per cent increase in billings to pounds 308m. "It's far cheaper to get new business from existing clients, you do it just by being good," he said, adding that 13 new accounts had been opened by existing clients.
Rumours continue to circulate about M&C Saatchi poaching clients from Saatchi & Saatchi.Possible candidates include Dupont, General Mills and Toyota. The most recent report was that BT's corporate account was about to move, which the telephone company promptly denied. "Those that wanted to leave have already left," said Ms Laing.
Mr Crozier said most of the rumours of accounts switching from his firm have been proven false, and blamed M&C Saatchi for starting them. "We're dealing with a campaign of misinformation. People call us and say 'We heard from the other side that so-and-so was leaving,'" he said.
Although he admits the rumours hurt, Mr Crozier insisted that Cordiant's recent rights issue, which all but wiped out its debt, has reassured clients that the company is not in decline. Globally, Cordiant had billings of more than pounds 4bn last year.