He even copied his screen costumes and pretended to be characters from his films, according to a former friend.
Michael O’Brien has told of Cunanan’s chilling infatuation with Cruise following the US launch of a nine-part “true crime” TV drama series: The Assassination of Gianni Versace.
It will air on BBC Two later this year.
He said: “Andrew wanted to be Tom Cruise and often emulated him.
“He’d go to Hollywood, hit the best places and drive around in a rented BMW in the hope of running into his hero.
“He had a vast collection of leather jackets but his favourite was a bomber jacket that looked exactly like the one Cruise wore in Top Gun.
“Andrew would look in the mirror and pretend to be the characters Tom plays in his movies.
“He really believed that one day he and Tom might actually be together.
“That’s how crazy he was about the whole thing.
“He lusted after him sexually and had his own ‘Cruise meter’ when it came to rating other guys.
“If somebody said to him a guy on the street was cute, he would say, ‘Oh, he’s OK but he’s no Tom Cruise.
“No guy is as cute as my Tom’.”
The TV series tells how gay gigolo Cunanan brutally killed four other men in three states before shooting dead 50-year-old Versace.
He shot the “designer to the stars” at point blank range on the front steps of his mansion in Miami Beach on July 15, 1997.
Cunanan, who went on his twisted murder spree after learning he had become infected with Aids, turned his gun on himself eight days later as police closed in following a massive manhunt.
Chillingly, he was just a short drive from a mansion owned by Cruise in Clearwater, Florida, when he took his own life while hiding out on a houseboat.
Detectives have said he left no note or other clues about plans to attack the actor.
But some believe he may have been trying to “stake out” the star’s East Coast home just as he had spied on Versace at a popular Miami club called Liquid, prior to assassinating him.
One witness now says: “At first, I figured he was just another young wannabe trying to attract Gianni’s attention.
“Now I know he was there planning the kill.”
Spokespeople for both Cruise and the Versace family have declined to comment, although members of the Italian fashion house have slammed US studio giant Fox for making the series without consulting it.
It said in a statement: “The Versace family has neither authorised nor had any involvement whatsoever in the TV series about the death of Mr Gianni Versace.”
The series stars Venezuelan actor Édgar Ramirez as Gianni Versace and Penelope Cruz as his sister Donatella.