It is understood members of the West Yorkshire Police Authority will today discuss the position of Chief Constable Sir Norman Bettison.
It follows allegations about his involvement in a police cover-up in the Hillsborough disaster.
The man who chaired the police authority until a fortnight ago is now calling for him to stand down now.
Mark Burns-Williamson resigned as chairman of the West Yorkshire Police Authority on October 7 to stand in the forthcoming Police and Crime Commissioner elections.
He said Sir Norman should go in the light of new information about his role in the aftermath of the Hillsborough disaster.
Mr Burns-Williamson was referring to shadow transport secretary Maria Eagle's claims, made in the Commons on Monday, that Sir Norman revealed he had been asked to help "concoct" South Yorkshire Police's version of events.
She used parliamentary privilege to make the allegations which were based on new evidence from a witness who discussed the disaster with Sir Norman. Ms Eagle, a Merseyside MP, alleged Sir Norman was behind a "black propaganda" campaign.
Mr Burns-Williamson, who is now Labour's candidate to become West Yorkshire Police & Crime Commissioner, said:
– Mark Burns-Williamson
In light of the new evidence given in Parliament yesterday I feel Sir Norman Bettison should stand down now in the best interests of West Yorkshire Police.
Sir Norman was a chief inspector with South Yorkshire Police at the time of the disaster.
He attended the match at Sheffield Wednesday's ground as a spectator but, after the disaster, he was involved in the subsequent force investigation.
The police authority has referred Sir Norman to the Independent Police Complaints Commission (IPCC) which is investigating his role.
The chief, who has always denied any wrong-doing, has also announced he plans to retire next year.