After 31-year-old Bjornsson, challenged Hall to a fight, The Beast replied: "1,000 per cent I'm going to sign those papers.
"CoreSports just offered me a seven-year contract, I have signed it already," Bjornsson said.
"Eddie Hall has been running his mouth now for weeks and I know he has been given the same contract.
"So Eddie, I just knocked out your record. And now I'm ready to knock you out in the ring.
"It's time to put your fist where your big mouth is, and sign the CoreSports contract.
"I'm ready. Are you ready?"
Hall wasted little time to respond to Bjornsson, revealing just how personal their rivalry has become.
"1,000 per cent I'm going to sign those papers," the Brit replied in a Facebook video.
The Mountain, famous for his 2.06m, 193kg frame, would be a terrible sight stepping into the ring against the 164kg, 1.91m Brit.
Combined, they weigh 357kg.
"And you know why I'm going to sign those papers… it's not the money, it's not the dead lift feud we've got going on, nothing to do with that," Hall said.
"It's because you called me a cheat at World's Strongest Man 2017.
"I can't put that to bed, I can't forget it. People may forget it, but you've never apologised.
"You think you should've won that year, regardless of the trophies or not, and you let people know that."