He and Bauer posed for photos together at The Sun’s Who Cares Wins Awards in November and Essex has often gushed about her after their performances on the show.
Asked whether he wanted to address the reports, he said: “I am open. I will answer.
“The truth is, obviously I am single, Vanessa is single. We go to the ice every day. It is cold. Got to keep each other warm. You know what I’m saying?
“So that’s it really. But, yeah, it’s all good.”
However, asked by Reid whether they are together, Essex appeared to backtrack.
He said: “No comment. Can’t confirm. But we are both single right now. We are taking it slow. It’s all good. I’ve not confirmed nothing.”
Reid said anyone watching Dancing On Ice will be able to see he has a “soft spot” for her, with Essex replying: “Of course I do. Vanessa is lovely, man.”
Sunday’s episode of Dancing On Ice saw former footballer John Fashanu become the first contestant voted off the show after ending up in the skate-off against Love Island winner Ekin-Su Culculoglu.
Fashanu, who was part of the Wimbledon team that won the FA Cup final against Liverpool in 1988, was eliminated after performing to Norman Greenbaum’s Spirit In The Sky with his professional partner, Alexandra Schauman.