Rockhopper executives told a conference last week that seven or eight companies were interested in bidding, according to investment bank Morgan Stanley.
A research note from the bank, which hosted the conference, also said the UK-based company could give up its lead role in the Sea Lion field it believes could have 1.3 billion barrels of oil in place.
Rockhopper would be willing to relinquish operatorship, if the farm-down interest was high enough, said the note.
The executives told the conference Rockhopper was giving would-be bidders access to its data because it needs money and expertise to fund the development in an area that is the subject of a territorial dispute between Britain and Argentina.
Mark Wilson, oil analyst at investment bank Macquarie, which also hosted an investor conference at which Rockhopper presented last week, said in a research note he expected the company to sell a 50 percent stake in its interests in return for the partner bearing all the cost of developing the project.
This limits the list of potential acquirers to well-funded companies, ideally with strong cash flows from production.
Shares in the company jumped by 10.0 percent to their highest level for over six months, trading at 302.5 pence at 1204 GMT, valuing the company at around $1.3 billion.
Analysts from Bank of America Merrill Lynch said Rockhopper was likely to see strong interest in the stake.
The significant exploration upside potential that the acreage still offers could prove a strong 'pull factor' for bidders - particularly those with limited exploration newsflow, they said in a note Monday.
Last year, Rockhopper unveiled plans for a $2 billion project to transform the remote Falkland Islands into an oil production centre and the firm said in October it had been approached by industry partners looking to co-invest with it on the project.
It said it planned to open an online data room toward the end of 2011 to allow interested parties to prepare a bid.
Industry sources said Edinburgh-based explorer Cairn Energy
Political concerns linked to a long-running sovereignty dispute surrounding the Falklands could put off some prospective partners, analysts have said.
Argentina claims the British-governed Falklands, and fought a war against Britain for control of them in 1982. It and some other South American countries refuse to allow vessels working on or supplying Falklands oil projects to put into their ports.
Falkland Oil and Gas
However, Chief Executive Tim Bushell said any company, such as BP or Spain's Repsol, who have Argentinian interests would most likely not be able to partner with it.
Industry sources said the support of South American oil producers such as Brazil and Venezuela for Argentina's claims on the islands they call Las Malvinas, means companies which have interests in those countries could also shy away from Falklands players.
FOGL said it was in talks with North American and European independent oil firms, and analysts said companies such as Anadarko
The potential return of US players to the area - Hess exited in 1998 - could significantly reduce the perceived political risk around the islands, said Bank of America Merrill Lynch analysts about Rockhopper, noting that Britain's Cairn Energy
Oriel Securities analysts said they believed significant upside could be generated for Rockhopper through a deal with a partner.
Rockhopper declined to comment.
(Editing by Erica Billingham and Andrew Callus)