The company, which is developing the Cobre Panama copper mine, said it has approached a number of groups who have expressed an interest in considering alternative deals involving Inmet or its assets.
Inmet president and chief executive Jochen Tilk said the board is going through an extensive process.
"We are looking at all possibilities," Tilk said when asked about the possibility of an investor taking a minority stake in Cobre Panama.
"We are not precluding or excluding anything specifically assuming that it could result in a superior transaction for our shareholders."
Inmet owns 80 per cent of the Cobre Panama copper project through Minera Panama SA, with the remainder owned by Korea Panama Mining Corp.
The total cost of the project is estimated at $6.2 billion, including $1.4 billion to be funded by Korea Panama Mining and $4.8 billion through Inmet.
Inmet said several unidentified groups are examining confidential information and discussions are ongoing.
First Quantum increased its offer last month to $72 per Inmet share, half in cash, half in stock, for a total offer worth about $5.1 billion.
It was the second time First Quantum boosted its cash and stock bid for Inmet, which rejected a $4.9-billion stock-and-cash offer in November.
Inmet shares were up 35 cents at $71.29 in trading on the Toronto Stock Exchange on Tuesday.
In rejecting the offer, Inmet said the proposal undervalued the company and its Cobre Panama project.
The company also pointed to the risk of swapping Inmet shares for those of First Quantum and the bidder's relative lack of experience building a mine the size of the project in Panama.
"Inmet investors also currently benefit from the highest copper reserves per common share amongst Inmet's peers which is five times better than what they will have in a proposed combined entity," Tilk said.
"These reserves will drive future growth, profitability and value creation for Inmet shareholders and should not go cheaply."
First Quantum has said that it has been approached by a number of Inmet's shareholders expressing interest in its offer.
The combination of the two companies would create one of the world's fastest growing copper producers with the potential to produce more than 1.3 million tonnes of copper annually by 2018, the company has said.
"We urge those of you who share our vision and support the idea of an open dialogue and exchange of information between our two companies, and we know that includes many of you, to likewise appeal to the Inmet Board to reconsider its current position and engage with us," First Quantum chairman and chief executive Philip Pascall said in a recent letter to Inmet shareholders.
The bid by First Quantum follows the sale of its operations in the Democratic Republic of Congo to Kazakhstani miner Eurasian Natural Resources Corp. for $1.25 billion.
First Quantum had written off the value of the assets in 2010 after its operations in Congo were nationalized by the government of the mineral-rich central African country.