The 28-year-old said he was keen on fighting fellow Briton Fury, whose licence was suspended by the British Boxing Board of Control after he relinquished his two world titles last year to focus on overcoming his mental health problems.
"It's Anthony Joshua versus the world right now, I have got to fight them all," he told Sky Sports.
"Eddie is right, as a promoter it works well for him, it works well for me and I think it works well for people who want to watch me and Fury get it on.
"I wish him the best of luck with what he's going through because we need to see him back in the ring. Eddie has been on the phone to Tyson, trying to make things happen and support his cause."
Fury, who has a 25-0 record, was also charged with a rule violation by UK Anti-Doping after a urine sample from February, 2015 showed traces of the banned stimulant nandrolone. He has denied any wrongdoing.
Joshua understands he must also fulfil his obligations with regard to mandatory fights as a champion against opponents including New Zealand's Joseph Parker and American Deontay Wilder.
"At the minute, the fighters who are closer on a championship level are the likes of Parker and Wilder," Joshua added.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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