After months of uncertainty, there is growing belief that a deal can be struck which could allow the troubled 140-year-old club to exit administration.
In a statement issued by the Foundation of Hearts group, Budge argues that financial support from the fans will be pivotal to the club's survival.
"The club needs your financial support to see us through the next two years," Budge said. "Your contributions are required to secure supporter ownership.
"My task, as I see it, is to ensure that when I hand the club over to you, the supporters, I will be handing over a club in good shape and with sufficient resources to face the challenges of the future."
Budge is the sole director of BIDCO 1874, the company that has thrashed out a £2.5m deal with administrator BDO, which could facilitate an exit from administration in the next two months.
"To achieve this the club needs investment over the next two years to stabilise and then build a solid financial base," she added.
"Some of you are asking how long you might be asked to contribute.
"Beyond that, and once ownership passes to the fans, it will be for you, the supporters, to agree the financial priorities of your club.
"These supporters have started to build the cash reserves to enable fans' ownership to become a reality, which will ultimately put an end to private ownership of our club."