Rumours have linked the Australian superstar with moves to European rugby union, as well as to British Super League clubs.
But the Eagles have confirmed that they would be able to match any financial offer that rival European rugby league clubs might make.
They would struggle to match offers from around the world, though, especially from French rugby union.
Ken Jones, Sheffield’s chief executive, confirmed to Australian network Fox Sports that his club would like to bring ‘GI’ to South Yorkshire.
“There’s obviously speculation going round, and a lot of rumour, and yes, us, like any club in the world, would be interested in signing Greg Inglis,” he said.
The Eagles apparently have the financial muscle to “blow any English Super League club out of the water”, according to the Fox report.
Jones also confirmed, however, that they would struggle to compete with any offers from European or New Zealand rugby union.
“No, we’re not in a position to do that,” he said, when asked if his club could match those kind of offers.
Australian newspaper the Daily Telegraph also quotes from emails to Inglis’s agent where Darren Johnston, Eagles director, states: “I am sure would be able to table an offer that is larger than any other rugby league club in the UK and would warrant further discussion.”