"John Oster is simply not for sale," Furneaux said.
"I sat next to Bob Murray at the Worthington Cup final last weekend and asked him several times about the player.
"I made the enquiry, and asked him again but he made it absolutely plain the player is not for sale."
Mariners player-boss Paul Groves was hoping a deal to sign him permanently would go through as Grimsby battle to climb off the bottom of the first division table.
"We're fortunate in that even if they wanted Oster back now they couldn't take him," Groves said.
"If they want to recall him the earliest date would be after our match against Rotherham on March 18th, so we have him for at least three more games."