Brighton owner Tony Bloom has made a multi-million-pound offer to invest in Hearts for a minority shareholding.
The proposal would see Bloom put £9.86m into the club for a 29 per cent stake via non-voting shares.
Hearts are owned by its supporters through the Foundation of Hearts, and a consultation period is now underway, with any deal requiring approval from more than 50 per cent of their members.
In a statement, the Foundation of Hearts have described the proposals as an "unprecedented opportunity for the club" and encouraged members to vote in favour of the plans.
They add that Bloom is personally investing in Hearts, and he believes "Hearts can disrupt Scottish football". The Foundation of Hearts also outlined that Hearts will not become part of a "multi-club system", and confirmed they will not become feeder clubs to Brighton or Royale Union Saint-Gilloise.
Talks have been ongoing for months, while Hearts announced a deal with Bloom's analytics firm last November.
Hearts used Jamestown Analytics - who also work with Brighton, Belgian club Union Saint-Gilloise and Como of Italy - to appoint Neil Critchley, who was sacked last month.
The company are helping Hearts find a new boss, and with transfers ahead of the summer window.
A statement from Hearts added: "Following the FOH [Foundation of Hearts] consultation process, an Extraordinary General Meeting of the club's shareholders will be called in order to formally approve the transaction.
"In the meantime, the transaction remains subject to entry into legally binding documentation, SFA approval and other normal course regulatory requirements."
Last year, Hearts' rivals Hibernian accepted a £6m investment from Bournemouth chairman Bill Foley and the Black Knight Group, for a 25 per cent stake.
The Easter Road club turned down other offers - including takeover bids - before proceeding with Foley.
When asked if some of those options could yet invest in another Scottish Premiership club and potentially prove to be influential, Hibs executive director Ian Gordon told Sky Sports News: "That might happen, but ultimately it's about Hibs and growing Hibs to be the best version of itself.
"Me and my family always have the club's best interests at heart. And when we make these decisions, it's always with Hibs on the front of our mind."
