Alley and Swayze met on the set of miniseries North and South in 1985.
At the time, the Drop Dead Gorgeous star was married to Parker Stevenson, and Swayze was wed to Lisa Niemi.
Alley said on Big Brother, 'When you get on the road and you’re doing a movie, it’s very easy to fall in love with your leading man. Very, very, very easy.
'Think about it…we shot North and South for a year. So for a year, you’re around this person…It’s just hard, I think.'
The actress then opened up about her run in with John Travolta, who was her costar in 1989 film Look Who's Talking and 1990 sequel, Look Who's Talking Now.
'I almost ran off and married John,' she confessed. 'I did love him. I still love him. If I hadn’t been married, I would have gone and married [him, too].'