The Italian dancer is allegedly dating Luba Mushtuk and the pair have performed together on a number of tours over the years.
Luba is a dancer and choreographer on the BBC One competition and she even danced with Giovanni, 27, on the show a few weeks back during Sheridan Smith’s performance.
But Giovanni’s close bond with his Strictly partner is believed to be making the four time Italian Dance Champion feel “uncomfortable” as she can see how much he “cares” for her.
“Luba and Giovanni are together. But she doesn’t like Debbie because of their bond — she feels how much Gio cares for her,” source told The Sun.
The insider added Luba wants their relationship to be public and has aspirations to feature on the show as a professional as well.
The source continued: “It’s also upsetting as she would like their romance to be out in the open. Luba is very keen to be on the show one day.
“She assists with choreography. But that means she has to spend a lot of time watching Giovanni rehearse with Debbie which can be uncomfortable for her.”
Debbie, 59, previously insisted she is just friends with Giovanni, despite pictures of them looking closer than ever behind-the-scenes.
The pair have constantly topped the leaderboard this series and Paul Daniels’ widow recently opened up about her “incredible bond” with her dance partner.
Debbie told OK! Magazine: “There’s a magic that is happening. The other dancers take the mickey out of us. He really cares, he doesn’t just care about me, he cares about everybody. He makes everyone feel special and that’s what Paul used to do, and that’s what I love about him.
“We’ve laughed about how similar we are. Why does it happen in life? I don’t know. We just have this incredible bond.”
Express.co.uk has contacted Giovanni’s representative for comment.