But he has admitted that the two of them are "strong-minded individuals" who have "had some conversations" during training.
It was claimed at the weekend that there had been tension between the pair ever since Week 1's dance off controversy.
Anastacia and Brendan were in the bottom two in the first results show where she was ruled unable to dance due to injury. As a result, Melvin Odoom was sent home.
The Sun newspaper suggested that Anastacia's ongoing injury had prompted rows in the training room.
"Brendan is not the most patient of dancers," an insider claimed. “They’ve had to tweak all their dance moves because of her injuries – they can’t even do any lifts or sudden turns.
“His previous partners like Natasha Kaplinsky, Lulu, and Kirsty Gallacher have dealt with his outbursts, but Anastacia doesn’t take any crap and fights back."
Writing in his Strictly column for DigitalSpy, Brendan responded to the rumours: "We've definitely had some conversations, I won't lie about that.
"I think we're both two very strong-minded individuals in a process, but we get along very, very well."
He added: "We're having a really good time, we're doing some really good work, we've had our share of controversy already - we didn't really need extra stuff!"
Brendan insisted: "I'm about as easy-going in training as I have been."
So that's that all cleared up!
Strictly Come Dancing is back next Saturday and Sunday night on BBC One.