Director Sergejus Fedotovas hinted on Saturday that takeover talks were taking place with a number of interested parties.
But the club continued talks with Supporters Direct Scotland at the weekend over increased fan involvement in the club, currently controlled by Vladimir Romanov's UBIG group.
A statement released on Monday stressed that supporter involvement remained a priority "provided it is productive and can demonstrate a secure path for the club's future wellbeing".
Fedotovas added: "We have a responsibility to protect the business and ensure that we give Hearts the best prospects for the future, even once the club has been sold.
"Our aim is to secure a solid and stable future for the club and we do believe that the supporters should play an integral part in this process.
"We must, however, not allow emotion to cloud sound business sense as our decision on who the club should be passed over to is a very important one when we are dealing with an institution as prestigious as this.
"Supporters can be assured that we will not rush this decision and we will maintain our positive communications with Supporters Direct, who have been integral in the overall discussions regarding possible supporter-control models."
In a statement on the Hearts website, SDS head Paul Goodwin said: "The meeting with Sergejus Fedotovas was productive and we agreed that the community ownership model was still an option that would be considered alongside any other offers that the club might attract.
"With that in mind we agreed to embark on a series of planning meetings over the coming weeks, working to see if a viable plan could be presented before the end of the season. The first of these meetings is scheduled for later this week."
- Sports & Recreation
- Supporters Direct