Fury, 27, was charged with a doping offence by UK Anti-Doping on June 24 after a urine sample taken in February 2015 - nine months before he beat Wladimir Klitschko to win his world titles - showed traces of the banned substance nandrolone.
However, Fury's legal team says the result of tests on the samples in March and May 2015 were contradictory.
The boxer's cousin, Hughie Fury, also a boxer, has also been charged.
The legal team for the pair said "Team Fury" had issued proceedings in the High Court.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"The two boxers strenuously deny taking any performance-enhancing drugs. However, during the last five weeks, leaks about these charges have appeared in the press and both boxers have been the targets of continual abusive language on Twitter," lawyer Lewis Power said in a statement.
UKAD declined to comment on Tuesday. Fury's legal team said an interim judgment was expected before Fury's rematch with the Ukrainian in October.
Fury beat Klitschko, 40, in November 2015 to win the WBA and WBO heavyweight titles.
(Reporting by Neil Robinson; Editing by Alison Williams)
