Fury used the micro blogging site recently to set out the names on his wish list for 2014. Browne was mentioned alongside American Deontay Wilder, European champion Dereck Chisora and (oh dear) veteran future hall-of-famer Roy Jones Jnr, and Big Daddy says he would gladly accept the challenge if the fight was offered to him.
He said: "All I can say is that his team should contact my promoter, Ricky Hatton, and I'll sign the contract tomorrow. The fans want to see this fight and I think it will be a war.
"He's said he's having a warm up fight in February. I'm in one corner to box for the Commonwealth title in early 2014. After that, I think we should fight each other.
"I promise Tyson that, unlike David Haye, I'll definitely turn up on fight night.”
Matt Clark, Browne's manager, believes a showdown with his fighter is the only realistic option on Fury's list: "He has already beaten Chisora, Jones is at cruiserweight and Wilder is likely the next available contender to the Stiverne v Arreola bout for the vacant WBC title. That leaves Big Daddy.
"Fury is ranked eighth by the WBC and Lucas 11th. It's a fight that makes sense and it's a great one for the fans.
"Lucas has expressed to me just how keen he is to box Fury next year. He respects him as a boxer, but he has plenty of fans that want to see him close Tyson's mouth."
Browne is no stranger to the UK, having boxed here three times as a pro. Last month, he snapped the unbeaten record of Sheffield's Richard Towers with a fifth round stoppage in Hull.