However, the pair - Salsa to One by Gloria Estefan - have rubbished them and lamented how close their bond is. Watch the video below...
During It Takes Two this week, host Janette Manara probed: "It honestly looks like you two are having the best time in rehearsals, getting along like a house on fire in rehearsals right?"
Shutting down any rift rumours, Amanda agreed and said: "Yeah we are, we are! We do and we laugh a lot, we have the same sense of humour which is really important. So we'll come out, work hard, and then we just laugh don't we."
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Giovanni, 33, added: "We do have a good time, but at the same time, obviously we have to do our dance. It's a difficult process, especially for people who have never done it Strictly before.
"I always say, 'It's a marathon, not a sprint.' The first few weeks are difficult, it is difficult, it's a lot of hours to train, a lot of hours to be concentrating but then when you get to Saturday and do what you did," the dancer added.
Earlier this month, rumours of a feud between them emerged when The Sun reported that Amanda had threatened to quit the show following a series of rows between the pair.
Amanda swiftly issued a defiant response to the claims. Taking to Instagram in a video shared ahead of Saturday's live show, Amanda said she was "ignoring the [expletive]," adding: "Just stop it. You know who you are.
"Stop it, grow up. No one gives a [expletive] and shut up, it's [expletive]. You know who I'm talking to as well, so come on, jog on. It's nonsense and you know it's nonsense."
Following the first show last week, professional dancer Giovanni praised Amanda's frame during their Viennese Waltz, a performance that scored them 29 points from the judges in week one.
Sharing a still from their dance showing the pair in hold, Giovanni wrote in the caption: "A moment of appreciation for this beautiful frame!" Tagging Amanda in the post, he added: "Smashed it," alongside a smiling emoji.