(CNN) -- San Diego Mayor Bob Filner, accused of sexually harassing women, will resign if the San Diego City Council accepts a proposed mediation agreement, local TV stations reported Thursday.
The resignation would be effective Friday, according to the stations, including CNN affiliate KGTV.
"It is still our understanding that his resignation is part of the deal that the San Diego City Council needs to sign off on during tomorrow's closed session," an official familiar with the negotiations told CNN's Lindy Hall.
The source emphasized that "until that happens, I don't believe you will see an official resignation."
City Councilman Scott Sherman said he had not seen the agreement, but is hopeful it includes a resignation, KGTV reported.
"The quicker he's out of office, the quicker it is to get back into city business," Sherman told the station.
Filner has been under intense pressure to resign in the wake of allegations of serial sexual harassment of women, including inappropriate touching, kissing and comments.
He has acknowledged improper conduct and recently underwent therapy. But he has previously resisted the resignation demands, saying his conduct was not enough to force him from office.
He even has been locked out of his City Hall office, though Filner indicated in a statement that he returned to work as mayor in that very office on Wednesday.
That was the same day that, according to Filner and others involved, three days of mediation talks yielded a tentative agreement.
City councilors and others have been reluctant publicly to divulge details on the deal, given the guidelines set by the judge overseeing the mediation talks.
Filner, for example, said in a statement Thursday, "Due to the confidential nature of mediation and settlement discussions, we are unable to comment or make statements about any of the terms." City Council President Todd Gloria, who is among the nine City Council members calling for a resignation, was similarly tight-lipped.
But that should change sometime after the City Council meets -- after a public comment period -- in a closed session around 1 p.m. (4 p.m. ET) Friday to decide on whatever pact is on the table.
"The business of the city of San Diego is being pushed forward as best we can," Councilman Kevin Faulconer said, adding that the last seven weeks have been "very difficult" but haven't stopped the city government from functioning. "We love our city."
Whatever the final deal is, lawyer Gloria Allred -- who represents Filner's former communications chief Irene McCormack Jackson, who has filed a sexual harassment lawsuit against her former boss, and who has spoken alongside several other accusers -- said Thursday that she hopes it includes not only his resignation, but no future payments to him for legal fees or otherwise.
"There should be no payoff for Mayor Filner," Allred told reporters Thursday. "His parting gift should be good riddance instead of a handout."
Allred said that while she took part in the mediation talks, neither she nor her client signed off on any deal, nor did she have details on it. She stressed that Jackson has not dropped her case against Filner, saying, "Our lawsuit is not settled."
News of the reported mediation agreement comes after yet another woman came forward to accuse Filner.
Businesswoman Dianne York told CNN that Filner put his hands on her buttocks during a photo opportunity that followed a meeting three months ago. York said there were witnesses to what happened. She said both her advisers and Filner's were in the room at the time.
York is the 18th woman to accuse Filner of improper conduct.
Jackson quit her job and sued the mayor in July, saying he subjected women to "crude and disgusting" comments and inappropriate touching.
Other women have accused him of touching their buttocks and putting them in a headlock and trying to kiss them, among other allegations.
And amid the storm of allegations, Bronwyn Ingram ended her engagement to Filner. She had campaigned alongside him during his run for mayor, and was known -- even though the two weren't married -- as the "first lady" of San Diego before ending their relationship.
But speaking Thursday alongside Allred in her first public comments since the scandal broke, Ingram said she now wants Filner to resign as mayor.
"I'm hopeful that tomorrow will begin a healing process," Ingram told reporters, "and that attention will return to the needs of the people."
CNN's Casey Wian and Greg Botelho contributed to this report.