'Mysterious Girl' singer Peter was Harvey's step-dad during his marriage to Katie between 2005 and 2009 but, since their divorce, Katie has accused him of not seeing Harvey.
Pete, however, gave an interview last week in which he said he recently had seen Harvey, whose dad is Katie's ex-boyfriend, footballer Dwight Yorke.
He had told Now magazine: "I see him a bit more now, which is amazing. He's just the best. I love him to bits and I want him to be happy."
Pete has now reconfirmed this in his weekly New magazine column, telling fans: "In an interview last week, I explained I've been seeing Harvey again. I don't see him all the time, but I see him at events like the kids' sports days."
"Also, there have been a few times recently where he's been to my house and I've been to his," added Peter. "Harvey will always be special to me and I just want him to be happy."
Harvey, 14, lives with Katie and her husband Kieran Hayler. The couple have two young children, Jett, two, and Bunny, one , while Katie and Peter share son Junior, 11, and daughter Princess, nine.
Peter's also dad to daughter Amelia, two, while wife Emily is pregnant with their second child.
In a recent interview, Kieran said he would like to adopt Harvey, explaining to OK magazine: "I've always thought it would be good because I'd like us all to be connected. He is my child at the end of the day. Why not actually make him mine, because he feels like he's mine anyway? He's my step-son no matter what happens."
Katie added: "I'd like Kieran to adopt Harvey."
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