Director Sergejus Fedotovas believes the current regime can successfully guide Hearts through their troubles after being given more time to pay their outstanding tax bill by Her Majesty's Revenue and Customs and rejecting a takeover approach.
The Edinburgh club said on Tuesday night that they had been granted until December 3 to settle their debt, with their owed amount of £449,692.04 being split over two payments.
The club have also provided HMRC with assurances that future payments would be made in a "timeous manner".
Hearts were last Wednesday served with a winding-up petition and given eight days in which to pay what they owed, putting their future in severe danger.
On another eventful day at Tynecastle an offer from the Foundation of Hearts consortium, led by Edinburgh businessman Alex Mackie, was dismissed out of hand, although Fedotovas admitted bids would be considered.
"We do believe we can steer through the current financial challenges we face," added Fedotovas, who revealed talks have been held with Supporters Direct over a supporter-led buy-out.
"When we move the club on it will be to the right people at the right time. At present we will continue these talks with Supporters Direct in parallel with maintaining the momentum that is gathering behind the club's share issue and other fundraising activities."
Hearts described the offer received from Mackie's consortium as "opportunistic".
Mackie, chairman of the Foundation of Hearts, said: "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.
"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 (Tuesday) been rejected by the current owners. We are now looking to continue our negotiations, which have always been constructive, with them."