The swimmer said that Smith, who won silver and bronze medals in gymnastics events at this summer's Olympics, has been "absolutely incredible" in the ballroom.
Speaking to Digital Spy at the Collar & Coats Gala Ball for Battersea Dogs & Cats Home last week, Adlington jested: "I saw him the other week and I was like, 'You should be good at dancing, you're a gymnast, you should have rhythm'.
"He's doing so well. When he did the Dirty Dancing routine the other week I just melted, because it's my favourite film."
Adlington also said that she understands gold medal-winning cyclist Victoria Pendleton's emotional breakdowns on the show, commenting that people always expect more of Olympians.
"It's so hard to try and do something different," she said. "It's so different swapping sports. Everyone just thinks, 'Oh you're an Olympian, you can do everything'. It's not the case. It's so, so difficult.
"I feel for all them guys [on Strictly]. I think it's definitely a challenge if you're not a professional dancer."
Adlington also stated that Olympians have a right to enjoy the celebrity lifestyle off the back of the Olympics.
"We only get to do it every four years," she argued. "Normally we're in training, we only get two weeks off a year so... it's kind of [right] that we should come [to events] and celebrate everything that's happened in the summer."
Adlington went on to reveal that she would like "amazing" Paralympic swimmer Ellie Simmonds to be named BBC Sports Personality of the Year next month.
"She's absolutely incredible," the athlete said. "She's so lovely as well. She's one of the nicest people and I'd love to see her up there for all she's achieved."
The 23-year-old was less optimistic about her own chances though, predicting that she "won't even be in there" with the nominees despite her two bronze medals from the Games.
Watch more of Digital Spy's chat to Rebecca Adlington below: