The Manchester-born fighter says a rematch with Deontay Wilder and then a unification clash with Joshua before the end of 2019 is possible.
But he questioned Joshua’s status as world champion after his dramatic draw with WBC title holder Wilder in Los Angeles at the weekend.
Fury was stripped of the IBF belt soon after his November 2015 win over Wladimir Klitschko then he relinquished the WBA and WBO titles amid his mental health problems and a drug addiction.
Joshua has since collected all three but Fury still feels he is the main man in the division and his belief was strengthened after climbing off the canvas twice in a thrilling draw with Wilder.
“They are just borrowed belts really,” said Fury. “I don’t really class them as world title belts because I’ve got them at home in my living room. They are all mine still.”
Asked if he thinks it is possible for a rematch with Wilder and then a fight with Joshua for the undisputed crown in the next 12 months, Fury replied: “Anything is possible with the right mentality for sure.
“I hope the best do fight the best because it is great for the fans and great for boxing. That is what we are here to do. We are not here to get a 100-0 record.
“We are here to put entertaining fights on while we are in the era and active.
“They are just borrowed belts really. I don’t really class them as world title belts because I’ve got them at home in my living room. They are all mine still”
“I wouldn’t like to go through my career knowing I didn’t fight the best. In my career so far I fought the best of the best.”
Fury made huge waves in America over the last week and the thrilling fight only served to raise his profile further.
The way he beat the count in the last has been immortalised already in memes and gifs across the internet and his career has been resurrected much like he was in that 12th round.
“The fight made a massive impact on America,” said Fury. “Everybody in America has heard the story of Tyson Fury, they’ve heard about the legend but now they’ve seen him.
“They now know why. Listen, it was a great fight and I’m sure the fans enjoyed it. It was a treat for the fans and refreshing to see two unbeaten world champions at each other, going toe-to-toe.
“I can be a star. I’ve got the engaging personality. I’m just being myself, I’m not trying to act up or anything. As you saw in there I was putting my hands behind my back and my hands in the air.
“Even when I was knocked down, I got straight back up and put my hands behind my back again. I am an entertainer, I would say.”
Fury insists he has no interest in thinking about a rematch for now or public recognition in the upcoming BBC Sports Personality of the Year awards.
When he beat Klitschko three years ago there were protests against his inclusion on the nomination lists after offensive comments about homos*xuals and women.
Instead his mind is only on his wife, Paris, and their young family.
“I’m going to go home and spend some quality time with my kids,” he added.
“I’ve been away from home for over two months and they’ve missed me. I’ve got a little daughter (Valencia Amber) there and she’s probably forgotten me. She’s only a year old.
“I’m just going to enjoy myself really, enjoy my family, enjoy my friends and enjoy my time off while I’ve got it because I’m back into training camp soon.
“I probably won’t go on a caravan holiday at this time of year but I might take the gypsy wagon out on the roads, the horse and cart.”