Foundation of Hearts confident they will meet bid deadline
The Foundation of Hearts also said they had two options to finance their bid.
Foundation chairman Ian Murray MP claimed that almost 4,000 fans have converted pledges of support into direct debits - 2,000 short of their target.
"We are nearly there and the Foundation will select the most appropriate route," he said.
Murray, the Labour member for Edinburgh South, added: "Should we be able to hit our own target for pledges we will in a position to draw down substantial capital to confirm a viable bid to take Hearts into the ownership of the people that matter most, the supporters."
The two funding options for the consortium remain confidential until after the deadline, but the group say both rely on securing as much financial support from individual fans as possible, coupled with partnerships with businesses.
Former Hearts captain Dave McPherson has also backed the Foundation's efforts.
"I want to offer my complete support," he said. "I hope the Foundation can secure the very final pledges requires to make the sort of bid to the administrators that they consider most appropriate to the future of this club."