The 61-year-old actress fell for her co-star on the set of the movie but couldn't act on her feelings because she was married to actor Parker Stevenson at the time, reported Daily Mail online.
"It took everything that I had, inside, outside, whatever, to not run off and marry John. And be with John for the rest of my life. He was the greatest love of my life," Alley said.
Travolta, 58, who is married to Kelly Preston, was single when they met and when Alley was asked why she didn't leave her husband for her co-star, she said the institution of marriage was very important to her.
The actress, who divorced Parker in 1997, said, "I feel like when you marry someone you're supposed to work hard at it, and you're supposed to make it work."