Paul Kane, who is fronting the campaign, was accompanied by prominent supporters - including Ian Blackford, managing director of First Seer and a former investment banker, and George Moore, a retired criminal lawyer.
Hibernian supporters have been demanding Petrie's resignation since the club was relegated from the SPFL Premiership following the play-off defeat to Hamilton last month and this week, Terry Butcher, was sacked as manager. Kane wants Petrie to fall on his sword and expressed surprise that the chairman was present at his meeting with Farmer.
He said: "I'd asked for this meeting with Sir Tom Farmer and took Ian and George along with me to put forward two proposals for the future of our club. It was important to open dialogue directly with the club owner and majority shareholder.
"I was very surprised Rod Petrie was present, especially after his disclaimer last week. Rod Petrie had told me then he was not involved in the running of Hibs any more since Leeann Dempster's appointment and now had a purely non-executive role.
"We discussed the two proposals and I will now submit a document outlining them in detail. At this stage I will respect Sir Tom Farmer's request for confidentiality but hope to bring the fans up to date at the soonest possible opportunity. I also made clear to Sir Tom [that] the Petrie Out campaign would continue. Rod Petrie has lost the confidence of the Hibs support and failed in his stewardship of the club. For Hibs to move on he should go now."
The process of replacing Butcher remains in its infancy with Ian Murray still the bookies favourite to succeed the Englishman
The club's former striker Colin Nish insists Murray is the perfect fit for the manager's vacancy at Easter Road. The towering forward was part of Murray's Dumbarton side that punched above their weight in last season's Championship, finishing fifth, confounding expectations that they would struggle as a part-time team.
The fact that Dumbarton were pushing for the play-off places right up until the closing weeks of the season was an achievement in itself given the tight financial restrictions the club operates under.
Nish said: "I think when any job comes around he is going to be linked with it, especially with his connection at Hibs. Even before the Hibs job came up, I always felt he was going to be the Hibs manager some day. The fact Hibs are in the Championship now and he's had two years in it and done a great job, I think you can see why he is favourite for it.
"The way we played as well, we always felt we were one of the better teams in the division and to do that on a part-time basis and on a limited budget, it just shows you what he could potentially do at a full-time club.
"It's a club he knows so well too, he knows a lot of people there and he will know the youth coaches as well. It does look like it's the perfect job, the perfect match really. He played for Hibs for over 10 years, he had his testimonial; he knows what it's all about and knows what the fans are expecting."
Nish has rubbished suggestions that Murray does not have the experience for such a high-profile role.
He said: "I think he is very calm and very sensible. I read the other day and that it's maybe a wee bit early and he's too inexperienced but he has probably got more experience in this division than anyone else mentioned for the job. It does not matter what age you are, he's always acted older than he is."