Hearts are looking to double a £6m fund to cover the estimated cost of building a new main stand at Tynecastle.
Hearts' majority shareholder Ann Budge hopes fans can drive this income via continued pledges to the Foundation of Hearts (FOH) and support of the club.
The transfer of Budge's shares to FOH would be delayed under the proposal.
"If contributions continued at today's levels, majority ownership would pass to FOH only eight months later than originally envisaged," said Budge.
"However, they would be taking over a club with everything in place to ensure financial stability and to position the club for continued growth.
"It is worth noting that, should the number of pledgers increase over this period, the original five-year plan could still be achieved."
Supporters and the club's on-field success, securing a third-place finish in the Scottish Premiership, form half of the £6m reserve, with the remaining £3m stemming from benefactor and commercial contributions respectively.
Budge has asked the Foundation of Hearts to postpone repayment of her loan for two years in the hope of raising the £3m for the main stand project during that period - current monthly income stands at £125,000.
Hearts also hope to raise £3m via a debenture scheme, which will soon be announced.
Budge has, in addition, offered to transfer 20% of her shares once £1.5m has been raised towards the stand and another 15% when the target is reached.
Her remaining 40% stake would be handed over when her £2.5m loan is repaid.
She has also offered to waive interest payments on her loan during the two-year period.
"This would effectively be my personal contribution of £300,000 to the main stand fund," she said.