Labour members have sought legal advice on making Ms Kelly a second offer, under which she would leave the council, or dismiss her. It earlier offered her£80,000.
Leader Richard Arthur said the council 'would like to settle the matter amicably' and confirmed an offer had been made.
Ms Kelly could not be contacted for comment.
Ms Winter claims she was discriminated against and victimised when the council considered her and a male manager for the top post in a reorganised housing service.
A Camden spokesman said the council had admitted it made a mistake, and had offered Ms Winter the job as manager plus an apology.
'We've since accepted we should have looked at only one person for the job and that was Christine Winter. But we are robustly defending the accusation of sexual discrimination,' he said.