The RuPaul's Drag Race judge, 51, described allegations of clashes between her and Pernice, 29, as "upsetting."
Her comments come after a story in the Sun which claimed the duo had been "locking horns" since they were first paired together in September.
A source was quoted as telling the newspaper: "Michelle has become quite unhappy at times. She has a fiery relationship with Giovanni."
In a tweet to the the paper, she said: "The articles about my partner and I have been upsetting. If anyone knows us, you would know how close Giovanni and I.
"Gio is my best friend in this competition, he is my rock and I trust him with everything.
"We have the most fun and laughs together and to suggest otherwise is just sad.
She added: "At this very moment, we are focusing on Blackpool and we are SO excited to share our magical dance with all of you!
"Thanks for the love and support!"
— michelle visage (@michellevisage)November 13, 2019
Last weekend's Strictly saw Visage and Pernice placed in the bottom two for the first time in the series.
They had been awarded 36 points by the judges, putting them in second place in the leader board, but failed to win over the public.
Visage and Pernice then had to dance off against BBC Breakfast presenter Mike Bushell and his partner Katya Jones.
Bushell and Jones danced their Paso Doble to Tamacun by Rodrigo y Gabriela while Visage and Pernice performed their American Smooth to I Just Want To Make Love To You by Etta James.
The judges then voted to save Visage and Pernice.
Strictly Come Dancing returns on Saturday, November 16 at 7.05pm on BBC One.