The council's service review committee agreed this week to start negotiations with Mr Winchurch to try to convince him to take on a permanent contract rather than retire.
Mr Winchurch had planned to leave in April, but agreed to stay when members had trouble appointing a successor.
A report from leader Ray Farrell said if the job was readvertised, a salary of£100,000 would need to be offered to attract the right candidates.
The cost of Mr Winchurch's retirement to the council would be a lump sum of around£30,000 plus another£10,000 a year in pension payments.
Readvertising the post on the same terms and conditions would cost the council£15,000 with another£5,000 for headhunting, 'with no guarantee of success', Mr Farrell argued.
When it first advertised the job last year the council specified a qualified lawyer. It got only seven responses. A second attempt with wider criteria netted a stronger field, but members still felt the candidates 'did not meet our requirements', Mr Farrell said.
Mr Winchurch steered the council through political turbulence in 1996 when Labour leader Dave Church was ousted from power and formed a breakaway faction.
When Mr Winchurch announced his retirement last year, Mr Farrell praised his relationship with members and said there was 'no point trying to keep people on if they want to go'.
Mr Winchurch declined to comment.