Independent studio Summit Entertainment, which is behind the popular Twilight franchise, could also be interested in Miramax, said the sources who spoke on condition of anonymity.
Disney has put Miramax up for sale because its library of mostly small, independent films does not mesh with the media giant's plan to overhaul its movie operations, a source close to the company said.
Disney is focusing on its own movie brand, as well as films made by its Pixar division and the newly acquired Marvel, and a distribution deal with Steven Spielberg's DreamWorks studio.
A spokesman for Lions Gate was unavailable for comment, while Disney and Summit declined comment. But Lions Gate and Disney are expected to report quarterly earnings on Tuesday, and will likely be grilled by investors and analysts about any possible interest.
Disney is asking between $650 million to $800 million for Miramax, home to art-house fare like Clerks and No Country for Old Men, said a source close to one potential bidder.
But a $500 million to $700 million price tag is seen to be more realistic, according to another source.
The potential sale of Miramax comes as the auction for another storied Hollywood studio, Metro-Goldwyn-Mayer, entered a second round of bidding.
While DVD sales have slumped and will likely hurt the price of any studio sale, the libraries of both MGM and Miramax still generate cash flow through licensing deals for television and other distribution channels.
The Weinstein Co confirmed its interest in Miramax, which Bob and Harvey Weinstein built 31 years ago and named after their parents Miriam and Max. The Weinsteins sold Miramax to Disney in 1993, but stayed on as co-chief executives until five years ago, when they left to form The Weinstein Co.
We are keen to look at the company and we will see what happens in coming weeks, said David Glasser, operations executive for the independent Weinstein Co.
The Weinsteins have been approached by financial partners to help them purchase Miramax and are reviewing the company's assets, according to a source familiar with the situation.
The New York Post reported that Lions Gate could initially bid from $500 million to $600 million for Miramax. This would be five times the studio's roughly $100 million in annual cash flow and about twice its $300 million in revenue.
But a person familiar with Lions Gate, home to the popular Saw franchise, said the company was price sensitive and not as aggressive as the Post story suggested.
As for MGM, its lenders late last month agreed to extend a debt forbearance to March 31, which gives the studio more time to find a buyer or explore alternatives including continuing to operate as a stand-alone entity.
Initial bids, including from Time Warner Inc and Lions Gate, had come in below $2 billion, sources have said.
MGM has said it is conducting due diligence with select bidders and that process is expected to run for the next several weeks. MGM is considering a prepackaged bankruptcy along with a sale, other sources familiar have said.
MGM is owned by a group, including private equity firms TPG, Providence Equity Partners, DLJ Merchant Banking Partners and Quadrangle Group, and media companies Sony Corp and Comcast Corp.
The studio has a library of more than 4,000 titles, including the James Bond and Pink Panther franchises.
(Reporting by Sue Zeidler; editing by Andre Grenon, Bernard Orr)