A war of words has developed among Scottish Socialists in the wake of Tommy Sheridan's News of the World defamation case win.
Tommy Sheridan won his £200,000 defamation case on Friday
Mr Sheridan described those who stood against him in court as "scabs".
SSP leader Colin Fox appealed for unity, but also accused Mr Sheridan of smearing fellow socialists who had "stood by the truth."
Lothian and Borders Police confirmed they were considering whether to mount a perjury investigation.
A police spokesman said: "We have received information from two people and we are in consultation with the Crown Office on whether or not to commence an investigation."
SSP minutes secretary Barbara Scott said she had gone to the police on Monday to submit her notes of the meeting at which it was claimed Mr Sheridan admitted visiting a sex club.
This followed speculation that there could be a criminal investigation into whether some people lied under oath during the three-week trial.
Ms Scott said: "I hope this will prove that we told the truth in court, and that it will prove Tommy Sheridan did in fact volunteer information that he was at a swingers club and that he's been lying in court."
Trial witness Katrine Trolle dismissed suggestions that she could have lied in court.
"I've got a really good job that I love," she said.
"I trained hard for four years at uni. I'm not ready to throw that away just to stand up and tell lies in court for nothing."
The SSP had called an emergency meeting on 9 November, 2004 after the Sunday tabloid printed details about the sex life of an unnamed MSP.
Carolyn Leckie and Rosie Kane both backed up the paper's claims
The minutes of that meeting were disputed during the case, with Mr Sheridan maintaining it was not a true and accurate record of the meeting and that, in fact, he denied the sex club allegation.
Carolyn Leckie, one of the MSPs who gave evidence which backed the paper's claims, told BBC Radio Scotland the SSP executive committee had agreed to send out dossiers to all party members which gave "their side of the story".
Ms Leckie said the 11 party figures who backed up the newspaper's claims in court, but whose evidence was rejected by the jury, had an "absolute priority" to clear their names.
"We need to win a battle for truth and integrity within our party and the wider public," she said.
She admitted the party was divided but said it was not inevitable that it would split in two.
However, Mr Sheridan said he would be reluctant to speak to the SSP members who spoke against him in court.
He told BBC Scotland: "There are miners in communities across Scotland who still don't talk to those who scabbed during the great strike of 1984/85.
"Twenty years from now it'll be the same with those who scabbed on me."
It now seems certain that Mr Sheridan will seek to regain control of the SSP.
Current convener Colin Fox said he would be happy to face a contest.
It is nearly two years since Mr Sheridan stepped down as leader of the party he co-founded, amid lurid allegations in the Sunday tabloid.
The Glasgow MSP brought the civil action against the News of the World after it printed claims that he had cheated on his wife, visited a sex club and participated in orgies.
A jury of six men and five women found in the MSP's favour by a majority verdict on Friday and Mr Sheridan was awarded £200,000 from the newspaper.
Watch a half-hour special programme, Sex, Lies and Socialism, on BBC One Scotland, at 2235 on Monday, 7 August. The programme will be available live and on demand online.