The guys have remained mum on the subject since Lovato left the tour, not addressing the matter until now, when they sent the singer/actress their well-wishes.
"I really haven't had any contact [with her]," Kevin said on "The Seven." "Of course, we wish her well in her recovery."
On the subject of texting, host Julie Alexandria asked Kevin if the rumor was true that middle Jonas brother, Joe, texted Taylor Swift back in 2008 to end the pair's relationship.
"No, that is not true," he answered about the two-year-old incident. "People have all their speculations, and she seems to talk about it in all her songs, so it's fine."
All drama aside, Kevin dished a bit about what the brothers are working on and looked ahead to some of the projects he and his brothers are gearing up to get cracking on for the new year.
"There's a lot of really cool things happening, a lot of new TV, a lot of new music and a lot of buzz about Joe's project, different things like that, so we're really excited," he said. "We'll probably lock ourselves in the studio for a couple of months and make an album that we love and we're proud of."
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