The former Miss Universe Australia, who has teamed up with Russian professional Michael Miziner in the reality TV show, said that it is still "early days" in their romance but that they are having fun.
Finch told New Idea magazine: "Michael and I have been dancing together for a couple of months now and we're having a great time.
"It's early days in our relationship but we're really enjoying each other's company and I guess we'll see where it leads."
The couple have been spotted holding hands and kissing after leaving rehearsals for the show in Melbourne.
Fellow contestant Jo Beth Taylor has also been romantically linked to her dance partner Dannial Gosper and has reportedly even been introduced to his parents.