WBC champion Fury's unification bout with Oleksandr Usyk, the holder of the WBO, WBA and IBF belts, had been due to take place in Riyadh later this month.
But the eagerly anticipated contest was postponed until May 18th in Saudi Arabia after the British fighter suffered a deep cut above his eye in training.
Fury expects to have a rematch with Ukraine's Usyk regardless of the outcome of their first fight, before facing former world heavyweight champion Joshua in one or two bouts and then Francis Ngannou, whom he beat in October.
"I keep hearing talk of people saying I should retire or I'm going to retire soon or whatever," Fury said on his Instagram feed on Wednesday, showing stitches above his eye. "I ain't retiring - I've got two fights with Usyk for the undisputed, twice."
Fury, yet to face Joshua, added: "Then I'm going to fight AJ (Joshua) at least once, maybe twice, if there's a rematch - if he wants one after the first battering I give him.
"Then I'm going to fight Ngannou again.
"That's just the start. There's five fights for you to whet your appetite. I ain't going nowhere. I'm 35 years old and in the prime of my life."
Fury has won 34 fights with one draw since turning professional in 2008.
His most recent fight was a controversial victory over former UFC mixed martial arts world champion Ngannou, making his professional boxing debut. Fury was knocked down but won on a split points decision.
Two-time former world champion Joshua is set for a non-title fight with Ngannou, also in Saudi Arabia, on March 8th.
The last undisputed heavyweight boxing champion was Lennox Lewis, when he beat Evander Holyfield in 1999.
