Fury, who is still facing an anti-doping hearing and is provisionally suspended, said on Twitter on Monday that he aimed to make a comeback against an unnamed opponent on May 13.
The 28-year-old has not fought since beating Ukrainian Wladimir Klitschko to become world champion in November 2015, subsequently pulling out of a rematch twice.
Warren, speaking to Reuters after a news conference to publicise an IBF world super-featherweight title bout on May 20 between American Gervonta Davis and Britain's Liam Walsh, hoped Fury could return.
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"I want to see him back in the ring as soon as possible but before that happens he's got a couple of issues to sort out," he said.
"There's a hearing set for early May and if he comes through that OK then he'll box.
"He seems to think that he will get his issues sorted out with UKAD (Britain's anti-doping agency) and let's hope that's going to be the case because we all miss him," he added.
Warren, whose BoxNation channel had been due to televise Fury's Klitschko rematch, said last October that the Briton had a 'self-destruct button'.
"It was a problem last year but he had problems himself and so we all got a bit of understanding of what was going on in his life," he said on Tuesday.
"Hopefully that's all behind him now and we can move forward and get him back to what he's doing which is being a great heavyweight boxer. Without a doubt he's the best heavyweight out there.
"I've got a lot of time for him...I'd like to be involved in moving forward and getting him back to where he should be, which is being the number one heavyweight."
Fury vacated his WBO and WBA belts last year, revealing he was seeking medical help, after telling Rolling Stone magazine that he had taken cocaine to help his depression.
Fury's licence was "suspended pending further investigation" by the British Boxing Board of Control.
He 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.
(Reporting by Alan Baldwin, editing by Toby Davis)
