Over the weekend, The Sun claimed that “tension building” was building between the two during rehearsals.
The publication also cited a “source” who said that the reigning Strictly champ and Radio 2 presenter “hadn’t clicked” during their initial training.
Appearing with Anderson on Strictly spin-off It Takes Two on Wednesday, Pernice took the opportunity to refute the claims.
When asked by host Janette Manrara whether they were “having the best time in rehearsals”, he insisted: “We’re having a good time.”
“Obviously it’s a dance competition at the end of the day, so we have to learn something, but there is no problem between us,” he continued.
“We are having a good time! So forget about what you’re reading, it’s not true.”
Anderson and Pernice performed live together for the first time last weekend where they received 23 points out of a possible 40 for their energetic Cha Cha Cha to Wham!’s I’m Your Man.
This Saturday they will be hoping to impress the judges with a Quickstep routine set to Barry Manilow’s Dancin’ Fool.
Strictly Come Dancing continues on Saturday at 6.30pm on BBC One.