An emergency meeting of the authority on Friday will discuss a scheme under which Miss Halford would receive a financial settlement over disciplinary matters in return for dropping her sex discrimination case at an industrial tribunal.
Miss Halford, 52, alleges that sex discrimination by the Chief Constable of Merseyside, James Sharples, the regional Inspector of Constabulary, Sir Philip Myers, the Home Secretary and the Northamptonshire Police Authority had held her back from further promotion.
The Merseyside authority would also drop separate disciplinary proceedings - Miss Halford was suspended over an alleged incident at a Wirral businessman's home - and she would then leave the force.
Pressure for a settlement has been mounting. The costs of the Manchester industrial tribunal, in its 39th day, are already thought to be more than pounds 1m, and the hearing could continue until April. There is also concern in senior circles about the damaging publicity resulting from media coverage of the case.
It is understood that during Friday's private meeting, members will discuss a report on the matter by Helen Mercer, the authority's solicitor. Lawyers representing Mr Sharples and the Home Office would not comment on the reports of a deal, first made in the Liverpool Echo newspaper yesterday and later confirmed by a source close to the police authority.
The newspaper said Miss Halford had denied any knowledge of such a deal. Her solicitor, Rex Makin, said: 'The story is very interesting but I can't confirm anything . . . Somebody has realised, and I think it must be the new Home Secretary, that these costs are escalating. I would put them at nearer pounds 1.5m than pounds 1m so far.'
Mr Sharples said: 'I'm advised by my lawyers that since Miss Halford has now closed her case, a number of decisions as to how we present our case have to be made. Consequently, there will have to be discussions between my lawyer and those representing other parties. I understand that the hearing has been adjourned in order for these issues to be resolved.'
The Home Office said last night that it had always been prepared to consider a settlement of the claim because of the massive costs involved.
A spokesman said: 'It has been well known that in the interests of the sensible use of money, we have always been prepared to consider some settlement.'