The country trio, who have just released their third album Own The Night, credited Twain with breaking down musical barriers across the globe.
Band member Dave Hayward told Digital Spy: "Her impact on country music internationally really shone a spotlight on the genre and allowed someone like Taylor Swift to do what she's doing today.
"She broke down barriers all across the world. Taylor and ourselves wouldn't have been able to do what we're doing if someone had not broken down those walls earlier."
Hayward revealed that he is "anxious" to hear what Twain's return to music will sound like and claimed that the band would love to work on new material with her.
He added: "We're huge fans and we'd love to write with her. If an artist wants to write we're down for that.
"The coolest way for us to meet somebody is to get to work with them and so I would love the opportunity to work with Shania. It would be great."
Lady Antebellum are on course to claim their first UK top five album this weekend with their new record Own The Night.
The group will play an intimate gig at London's Union Chapel on Friday (October 7) to help promote the LP.
> Lady Antebellum interview: 'We're blown away by UK success'
Watch the music video for Lady Antebellum's 'Just A Kiss' below: