The 28-year-old said in a post on social media he was aiming to return on the Billy Joe Saunders-Avtandil Khurtsidze undercard.
Fury, who has not fought since he beat Wladmir Klitschko in November 2015, had his licence revoked in October as he dealt with mental health problems.
He initially wanted to return in May but the British Boxing Board of Control told the BBC he was still suspended.
Fury posted that he was travelling to Marbella to train for the Saunders-Khurtsdize bout, which is scheduled for 8 July.
He vacated his WBO and WBA world heavyweight titles a day before his licence was suspended, saying he was unable to defend them because of his health.
The BBBofC said at the time that Fury's licence was suspended "pending further investigation into anti-doping and medical issues".
He would have to appear before the board to be given permission to fight.
Former heavyweight champion Tyson Fury is targeting a July return to boxing.