29-year-old Fury, has not fought since November 2015 when he outpointed Wladimir Klitschko for the WBA, IBF and WBO belts. Since then, Fury has failed a drug test - which he is protesting about - and claims to have had problems with mental health and drinking too much alcohol.
He has resumed training and plans to make a ring return in spring 2018.
"He's [Fury] just awkward, tall, and I think he's a bit of a nut-job, to be honest with you," said Joshua, who is on holiday at Jumeirah Al Naseem in Dubai.
"I think he's just got a bit of a screw loose. Any man with a screw loose, they just have a little something that you can't put your finger on. So with Fury it would be tricky to figure him out."
Joshua and Parker's teams are in negotiations on a purse split, but Joshua is upset about a press conference held by Parker and his promoter David Higgins earlier this week in which they named fighters to have floored the Briton in sparring or as an amateur.
"The fight's still not made; he's investing his time in the wrong areas," said Joshua, who has knocked out all 20 professional opponents since winning 2012 Olympics gold. "Does he want publicity? Is it a PR stunt?"
"It's not about worrying about who we fought or who we fight because I've worked my way through the ranks - from my 15th fight I competed for the heavyweight championship of the world. 15 fights in, three years as a professional.
"I think I've defended it now four or five times, with no complaints. Against one of the all time greats [Klitschko], we came together and put on a great show so what's so difficult with fighting this little kid [Parker], doing press conferences talking a load of rubbish. I don't get it; we work with people. It's just very unprofessional of them.
"But it's a shame because boxing has so much credibility. The heavyweight championship is a really well-respected title to have. But stuff like that takes away from the crème de la crème of the sport."
Joshua, who lives in North London, says he would have no problem knocking out Wilder, while Fury, from Manchester, is the toughest fight available to him.
"Wilder, I'd knock Wilder out. It would take a bit of time, but I'd definitely knock him out," said Joshua.
"Parker would take a bit more of a pasting, but I'd get to him. Wilder, I'd knock him out with one shot. Not like I'd go in there and bang, but when I catch Wilder, I'd definitely knock him out.
"And Fury would be a real breakdown job, a real gruesome-type fight. Kind of like that Klitschko fight - I'll go to hellfire and back to get the win." THINK YOUR FRIEND WOULD BE INTRESTED? SHARE THIS STORY USING ANY OF THE SHARE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>