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.
Last year Club 9 advised Bill Miller, who withdrew as preferred bidder for Rangers, on his offer for the Glasgow club when they were in administration.
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".
The Italian led Livi into administration and ultimately demotion to the Third Division in 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.
"Under the right guidance, the club has the potential to be successful both on and off the pitch, and it is encouraging to see that a number of prospective owners have clearly recognised this.
"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."
Hearts revealed they had broken through the 10,000 season-ticket barrier earlier this week, with the financial boost allowing them to reject an improved offer for midfielder Jason Holt.
The club confirmed they had turned down a "second bid from a Championship club" following reports Nottingham Forest had renewed attempts to sign the 20-year-old, who scored three goals in 23 first-team appearances last season.
Hearts managing director David Southern told the club's official website: "It's thanks to the fantastic fundraising efforts of the supporters that we are in a position where we do not have to sell our best talent for below market value.
"Gary Locke has a small squad and will face a challenging season so to rid him of another player, and such a talented one as Jason Holt, would not benefit him or the club as a whole."