The former heavyweight champion announced his retirement in August 2017 after he was knocked out in the 11th round by Joshua at Wembley earlier that year.
Joshua, meanwhile, has been searching for a new opponent ahead of his first fight in the United States after Jarrell Miller was forced to pull out due to three failed drugs tests.
In March, Joshua’s promoter Eddie Hearn revealed that Klitschko had held ‘exploratory’ talks about a possible comeback.
And in a post to fans on social media on Monday, the 43-year-old suggested his boxing career is not over and that he wants ‘to become a champion again’.
Klitschko posted on Twitter: ‘Although, I didn’t win the titles on April 29th 2017, for me, it was one of my best days in my long boxing career (so far).
‘Thanks @anthonyfjoshua for being the perfect opponent and part of my obsession to become a champion again! #obsessed.’