Reports had suggested that the pair had begun dating after Smirnoff split from fiancé and fellow dancer Maksim Chmerkovskiy in September.
Speaking to OK, he said: "It's completely false. We're two people who like to be out and about.
"You would have seen us out already. We would have been caught. There's nothing going on!"
Smirnoff added: "We're doing the time without doing the crime!"
Carter recently joked that he had been "respectfully rejected" by Dancing star Chelsie Hightower after he admitted to having a crush on her.
> 'Dancing' Week 4 - What the judges said