The deal was offered when Toon were in the process of being sold to a Saudi-backed consortium, whose offer has since been withdrawn.
However, owner Mike Ashley remains committed to completing the takeover, which could reward Newcastle with new owners who would be willing to spend heavily in the transfer window.
"During the period in which there was talk of the possible purchase of Newcastle by the Sheikh's fund they called my agent, Alessandro Moggi," Immobile told Corriere Dello Sport.
"Then the Premier League did not approve that proposal, or the fund withdrew, I don't remember well. I know they were also looking for an Italian coach, [Massimiliano] Allegri or [Luciano] Spalletti."
"I intend to tie myself to Lazio forever. The renewal will be for three years, so the contract will expire in 2025 when I turn 35," said Immobile.