Chairman George Foulkes hopes Hearts' major shareholders do not price out any potential buyers for the club.
Foulkes hopes shareholders put the club first
Lithuanian Vladimir Romanov has had discussions with chief executive Chris Robinson, former chairman Leslie Deans and Scottish Media Group.
Each party owns approximately 20% of the club's shareholding.
"It's important that the shareholders are realistic about their expectations when it comes to the possibility of selling their stake," said Foulkes.
Speaking to the Edinburgh Evening News, Foulkes added: "Hopefully people put the interests of the club first.
"Mr Romanov has some good ideas about the future of Hearts."
Serghei Fedotovas, a representative of Romanov, told the Edinburgh Evening News: "Things will become more clear next week when there should be a development.
"One of the reasons we are attracted to Hearts is that they are in Edinburgh, which is a growing prospective financial centre.
"This was one of the main things that we discussed before making an approach."
Hearts supporters will be hoping that any new investors in the club will prevent the agreed sale of Tynecastle to property developers Cala Management.
The terms of the £20.5m deal allows Hearts to pull out of the sale if a financially viable alternative is found before 31 January 2005.