The 41-year-old Klitschko may move into politics rather than continue his fighting career but, if he does carry on, the unbeaten Fury could be in line to take him on.
His fellow Brit David Haye is also hoping to lock horns with the elder of the two Klitschko brothers who dominate the heavyweight division.
But Peter Fury thinks Tyson may be able to jump ahead of Haye and told the Manchester Evening News: "If we can get Vitali Klitschko for March, then we will.
"We are happy with that, I'm happy to sign up for it. We are ready if Vitali decides to fight on.
"I can see Tyson winning and keeping hold of the world title. He is developing into a serious world class fighter.
"He has so much more to give, now he just needs polishing because the hard work has been done. It's taken a year to get the technique right and he's on the world stage now.
"We are hoping to take a world title in 2013 and my aim is for him to stay at the top. Tyson will be recognised as the best."
Peter Fury is also excited about his son Hughie, who won the Youth World Championships in Armenia last month and is regarded as a top heavyweight prospect.
"I said from day one that I'm going to groom the next two Klitchkos," said Peter Fury. "That's my ambition, my aim.
"They are both similar sizes and both strapping lads. They are on the right course. Tyson won the bronze in the amateurs and now Hughie has won gold.
"My ultimate aim is for him to be a world champion but he will have a great amateur career and get great experience."