Olivia Newton-John was apparently a Swiftie -- at least that's what her rep says, telling us the late singer would've gotten a kick out of these Taylor Swift's 'Grease' throwback photos.

Michael Caprio, Olivia's publicist of 25 years and counting, tells TMZ ... Olivia "would be tickled" to see all the childhood pics of young Taylor playing Olivia's famous character in a school production of the hit musical ... which just surfaced earlier this week.

Olivia's publicist adds ... she "had the greatest respect for Taylor as an artist and she was a fan of her talent." So, the fact Taylor was paying homage to her in her youth is kismet.

As we reported ... some old photographs of Taylor in character as Sandy is making the rounds ... it's from June 2000, long before Taylor was the biggest star in music.

Funny enough, Olivia and Taylor actually crossed paths when ONJ was still alive ... Michael says Olivia took a group of girlfriends to see a Taylor concert in Miami in 2010, with Olivia raving about Taylor's performance.

Michael recalls Olivia telling him she thought "Taylor was such a sweet, talented and smart girl."

Sounds like the feelings are mutual ... Michael says Taylor's got a vintage concert t-shirt from Olivia's 1982 Physical Tour in her wardrobe. On its face, they were big fans of the other.

Ya gotta love it ... Taylor was more than likely hopelessly devoted to the part, and it seems Olivia would've really appreciated that.