The Foundation of Hearts, an alliance of supporters groups, was the first to submit its bid 24 hours before the deadline and another two groups followed them on Friday.
Joint administrator Bryan Jackson said: "We can confirm that we have received three bids for Heart of Midlothian FC.
"To preserve confidentiality, unless disclosed by the bidder themselves we will not be naming the parties."
A potential rival to the Hearts fans emerged earlier this week in the shape of a group headed by Borders businessman Bob Jamieson and backed by American investment firm Club 9 Sports.
Former Livingston owner Angelo Massone is also reported to have made another offer for the club.
Hearts rebuffed a bid from the Italian in November last year, stating they felt he "may not be the right person to take the club forward".
Under the Italian, Livingston went into administration and were demoted to the Third Division during a disastrous year-long spell in 2008-09.
The Foundation of Hearts bid is backed by more than 5,500 supporters, who have set up direct debits to fund their offer.
Jackson urged fans to be patient as events in Lithuania are complicating the process.
Hearts owe about £25million to their two major shareholders, Ukio Bankas and UBIG, both of which are insolvent, but the latter has not had an administrator appointed.
Jackson said: "Further discussions will now take place with the bidders and also with the legal representatives of the administrators of Ukio Bankas. We would then hope to be in a position to name a preferred bidder.
"At this stage we cannot say how long that process will take.
"The CVA (Company Voluntary Arrangement) will need the support of the other major creditor and shareholders, and there may be a delay in securing that support while administrators are appointed to those entities.
"Therefore the sale process may take some time before a deal can be concluded and the club exits administration.
"In the meantime, we will continue to run the club and support the manager in his preparations for the forthcoming season.
"We all want the club to exit administration as quickly as possible but it's important not to get carried away: we're still much closer to the start of the process of concluding a sale rather than the end. We ask fans, players and staff for their continued support and patience."