Gaga, 25, recently performed on the show and was seen comforting Kitty, 27, after she was voted off.
It's claimed the pair spent an hour together after the show and had a drink together.
A source said to UK newspaper The Sun: 'Kitty was still emotional so Gaga poured her a glass of wine and asked her to join her in prayer. She stooped on the floor, putting her hands in a prayer position.'
The source added: 'She went on to say how she'd be on the road a lot next year and thinks there could be an opportunity for them to collaborate.'