Administrators BDO on Friday confirmed they had received three bids for the club ahead of their deadline for first offers.
Joint administrator Bryan Jackson revealed they would need to work with the interested parties and the administrator of Ukio Bankas, which holds securities over Tynecastle, before being able to announce a preferred bidder.
Jackson's task is complicated by the fact that UBIG, which like Ukio is both a major creditor and shareholder and also insolvent, is still in the process of having an administrator appointed. And he estimated it would be "three or four weeks" at least before a decision can be made.
The Foundation of Hearts was first to submit its bid after more than 5,500 supporters opened up direct debits to raise funds for a potential takeover. Their rivals appear to include a consortium which is backed by US-based Club 9 Sports, which was involved in a 'newco' bid for Rangers last year.
Massone has also continued his interest in Hearts after having a bid knocked back last year when the club decreed he was not the right person to take them forward.
The Italian lawyer was part of a group that bought then Scottish Premier League side Livingston in 2008. One year later Livi were in administration and had been demoted to the bottom tier, before Massone yielded to public pressure and sold his shares amid fears the club would be liquidated.
Former Hearts coach Peter Houston believes the club would be safe in the hands of supporters.
"I think it would be best if Hearts got back to being a community club and I think the fans' bid would probably suit most Hearts fans," the former Dundee United manager said. "Whether it's the right bid or not I don't know because I'm not party to what the other bids are.
"But, certainly, Hearts fans would want to see them looked after by Hearts supporters."