The Watford-born boxer retained his WBA and IBF titles when he overcame Carlos Takam at the Principality Stadium last month.
And his promoter, Eddie Hearn, has since revealed talks are ongoing over potential fights with WBC champion Deontay Wilder and WBO title holder Joseph Parker.
If Joshua beats Wilder and Parker he can become the first heavyweight to hold all four titles at once.
And the 28-year-old believes that feat would mean parallels being drawn to boxing legends Tyson and Ali would be fair.
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Anthony Joshua vs Deontay Wilder: AJ fires warning to Wilder
Anthony Joshua: DEFEAT would make me more like Muhammad Ali
At the minute I'm a prospect, but I keep a lid on it because there's a long way to go
Anthony Joshua opens up
"100 per cent, because we've done something credible and tangible," Joshua told Dubai Eye 103.8 after being asked if he would compare himself to Tyson and Ali if he unified the division.
"The proof is always in the pudding, and once I've got something I'll talk about it.
"At the minute I'm a prospect, but I keep a lid on it because there's a long way to go."
Joshua also opened up on the work that's gone in to putting him on course to fight for all four belts.
DUBAI EYE 103.8
Anthony Joshua has been tipped to fight Deontay Wilder, Joshua Parker or Tyson Fury next
Anthony Joshua has had his say on when he can be compared to Mike Tyson and Muhammad Ali
"It has been four years in the making," he added.
"We have been listening to what people want and they want to see who is king of the heavyweight division.
"I'm embracing everything coming my way this year."
Fellow Brit Tyson Fury has been talked up as a potential opponent for Joshua should Wilder and Parker decide to fight each other next year.