Supporters Direct Scotland's Paul Goodwin says he and Hearts director Sergejus Fedotovas had "positive dialogue" on Wednesday.
That dialogue is in relation to a proposed fan-led takeover of the club.
However, those talks have not reached the stage of knowing what price Vladimir Romanov seeks for the club.
"I think there'll be major progression in the foreseeable future," said Goodwin.
"The main focus of today was to get into positive dialogue and that happened."
Supporters Direct Scotland are the organisation backed by the Scottish Government to promote fan ownership and sustainable finances in Scottish football.
Goodwin stressed that they are merely the "facilitators" of the process and will relay relevant information to bidding groups.
"It's not us that's doing any bids," he said.
"We're looking at options available to see if there's a way the club could be operating in a community ownership basis. So we're giving advice on that."
However, Goodwin admitted the price to secure ownership of Hearts has not yet been revealed.
"The devil will be in the detail," he said. But at this particular stage it's really trying to get to the principles.
"The fact we've met with Hearts four times now would be some sort of assurance for the fans that this is something that's being looked at seriously.
"At some point we'll get to a place where we get all those fan groups together and say 'here's the options', but we're a bit away from that just now."
On Tuesday, Hearts said they had rejected a "note of interest" in the club from the Foundation of Hearts consortium led by businessman Alex Mackie.
A Hearts statement stated that Mackie's bid "demonstrates a staggering misjudgement of the value of the club".
The statement also went on to claim the bid showed "a worrying lack of understanding of the situation".
Earlier, the group told BBC Scotland they had made a formal bid after having a "constructive dialogue" with a view to buying Vladimir Romanov's share in the Scottish Premier League club.
And, in conjunction with Supporters Direct, they hoped to provide a vehicle for fans' ownership and planned to speak to the Hearts board on Wednesday to discuss their bid.
Foundation of Hearts chairman Alex Mackie said that it had been discussing plans for the last two years.
Mackie is unsure how much it would cost to buy out Romanov but believes it would be significantly less than
the £50m price tag that the Lithuanian put on the club last year.
Last month, Hearts invited fans to
buy shares belonging to Romanov in a bid to support the long-term future of the club.
Financial problems at the club and a tax demand for almost £450,000 has put Hearts under threat and Hearts supporters have been urged to find £2m to help the Edinburgh club survive until the summer.
Fedotovas says he will hold further talks with Supporters Direct
The club have reiterated their intention to offer supporters an opportunity to take control of the club and that they had entered into talks with Supporters Direct.
"The proposal has no consideration of cash for the shares of the club, even if the debt is removed completely," said a club statement.
"At best, it is opportunistic, an attempt to exploit what is a difficult financial situation at the club.
"No evidence was provided on how the club would be operated and resourced after any potential purchase."
Hearts say they remain open to genuine offers but would continue to with their share issue and other fundraising events.
"When we move the club on, it will be to the right people at the right time," said Fedotovas.
"With this in mind, we have held positive initial discussions with Supporters Direct and we have asked this organisation for further talks on how we might be able to structure an appropriate supporter-led buy-out of the club."
Mackie responded by stressing that fan ownership was the goal of his own group.
"We have been working for the past two years to try to convince the current owners that a transition to proper fan ownership was the way forward," he said.
"This has involved a great deal of work behind the scenes and, at the weekend, we did make an offer to the club.
"However, we have to announce that this initial offer, which included the Foundation paying the £450,000 bill to stop the winding-up order, has today been rejected by the current owners.
"We are now looking to continue our negotiations, which have always been constructive, with them.
"What we aim to deliver is a structure whereby fans have majority control, not the minority percentage which is currently being proposed by the current owners, and are involved in the management and running of the club.
"The foundation was set up by a group of businesspeople, all Hearts fans and all working in their own time and at their own expense, and we have the backing of the key Hearts supporters' organisations for our plans."
Goodwin confirmed that Supporters Direct Scotland shared in the Foundation of Hearts' objectives.