Reid and Price married in 2010 and separated in January last year. She was previously wed to singer Peter Andre from 2005 to 2009.
Asked if Price's previous marriage 'cast a shadow' over his relationship, Reid told Now: "Yeah, I think that's fair to say."
Price accidentally referred to Reid as 'Pete' on TV in May 2010 and he confirmed that it had happened in private also.
"Yeah, it did," he confirmed. "It just slipped out once or twice. When she got angry, she'd call me Pete."
At the time, Reid said that he "didn't have a problem with it at all", adding: ""I've called ex-girlfriends the wrong name before... she was talking about Pete just before, so it is ridiculous to make a big deal of it."
Of Price's new engagement to current partner Leandro Penna, Reid added: "I'm best out of it... There are lots of things that happen in this world that aren't ideal."
Reid is now engaged to former Celebrity Big Brother winner Chantelle Houghton, who is pregnant with the couple's first child.