Lewis made the announcement following reports in multiple American MMA media outlets that the heavyweight showdown was being targeted as the headline act for the UFC's return to Vector Arena.
However, the UFC is yet to confirm the bout.
"My next opponent is Mark Hunt in New Zealand June 10th," Lewis tweeted.
Hunt (12-11-1-1) is coming off a third-round TKO loss to Alistair Overeem earlier this month and has to wait until April 19 for a medical clearance after suffering a leg injury.
