The world boxing champion, who lives in the resort, was being interviewed by the former Manchester United star for Neville's YouTube show, The Overlap.
The famous pair were joined by a camera crew for a stroll along the beach as the 32-year-old heavyweight chatted with Neville ahead of his hugely anticipated title fight against Deontay Wilder in October.
The 6ft 9ins boxing champion, dressed in a white t-shirt and black trousers, towered above Neville as the two walked side-by-side on the sand, shadowed by a small production crew.
The champ is back home in Lancashire with his family after spending recent weeks preparing for his big fight at a training camp in Las Vegas.
On Sunday (August 1), the Furys were reportedly spotted enjoying a meal and some ten-pin bowling together at Soul Bowl on the Promenade.
The Overlap, which is free to watch on YouTube, sees Neville interviewing some of the biggest names in world sport, with stars reflecting on their careers and the challenges they have overcome to achieve their dreams.
Just last week, Neville interviewed Britain's other world heavyweight boxing champion and Fury rival, Anthony Joshua, as he prepares for his own upcoming title bout against Ukrainian contender Oleksandr Usyk in London next month.
In the interview, Joshua described Fury as one of his "enemies" and said he would be willing to fight him even if the pair's world heavyweight titles were not on the line.
Joshua and Fury agreed to a blockbuster battle for all the world belts this summer, but the fight dramatically fell apart when the boxing authorities ordered Fury to defend his WBC title against Deontay Wilder instead.
Asked by Gary Neville whether he respects Fury as a fighter and a man, Joshua said: "I don't know. I like [former opponent] Wladimir Klitschko, he's cool.
"I don't know. I don't look at anyone in my industry like that. They are just people that I want to fight.
"I haven't got no time for none of them. I'm not friends with no one. They are all enemies at the end of the day."
The Tyson Fury episode of The Overlap is expected to be available to stream on YouTube later this month.