The Briton, who climbed off the floor twice on the way to a controversial draw in his fight for Deontay Wilder's WBC heavyweight title in Los Angeles on Saturday night, is planning a family holiday before discussing his next move, but he hopes to have a rematch with Wilder next year, which could set up a clash with Joshua for the undisputed world title.
On Saturday, both Wilder and Fury made strong cases for 2018 Fighter of the Year honors.
Joshua has a Wembley date booked for April against an opponent yet to be named, with lengthy public negotiations failing between he and Wilder previously.
Fury largely outboxed Wilder for the first half of the bout until a short right hand caught him on the temple and dropped him early in Round 6.
Fury doesn't think Wilder is as keen as him on a rematch. ALL ACCESS: WILDER vs. FURY EPILOGUE goes behind the scenes, into the locker rooms, corners and inner circles as Fury aims to complete a storybook comeback and Wilder looks to continue his reign as the baddest man on the planet..
Reflecting on the judging, Fury would blast Alejandro Rochin, the judge who voted for Wilder, "Rochin, you need sacking, or to go to Specsavers, mate" claimed the lineal heavyweight champion.
PETA asks people to stop using 'bring home the bacon'
The activist group, People for the Ethical Treatment of Animals (PETA), has a problem with phrases it says are anti-animal. In place of taking "the bull by the horns", how about taking "the flower by the thorns?" Instead of: "Beat a dead horse".
Tyson Fury and Deontay Wilder will have reversed roles when, as expected, they meet next year for a re-match of their instant classic heavyweight bout. That has always been the fight we want because he has the last belt.
"I just showed the world tonight, and everyone suffering with mental health problems, you can come back, and it can be done". You'd have a 90,000 gate at Wembley, so you're talking serious money. They've said they do.
If the mega fight does come to fruition it would see the victor - as long as there's no draw at this one - claim the WBC, WBA "super", IBF and WBO Heavyweight belts. They said it wouldn't go ahead - well it did go ahead, didn't it? I genuinely feel sorry for Tyson.
"I'll give you a fair one when your (sic) ready!"
"That's as bad a decision as the first Lennox Lewis-Evander Holyfield fight (in 1999), but who am I to say anything? Now, Fury's the people's champion".