His licence was withdrawn "pending further investigation" by the British Boxing Board of Control last October.
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.
"After thinking long and hard about my return I will not be applying for a BBBOC boxing license. After the way they have handled stuff. No thanks," the Briton wrote on Twitter.
Fury appeared to have retired last year, only to retract his statement before giving up his titles, saying he wanted to deal with mental health issues.
In March 2017, Fury suggested he could make a comeback and when compatriot Anthony Joshua beat Klitschko at Wembley the following month, the new world champion said he wanted to fight Fury, a challenge which was accepted on twitter.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
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