The pair spent the night together in the penthouse of the Miami Beach Hotel last month, where the X Factor judge was filming the video for her debut solo single, the Sunday Mirror reports.
"He's head over heels for Tulisa and can't stop talking about the time they spent together in Miami. He's very much hoping things progress into a relationship. But Tulisa's mortified by the whole thing and is furious that Mark's been opening his gob to everyone and anyone about their snog," a source said.
"She didn't think it was anything but a laugh after a few drinks. Mark on the other hand definitely wants more than just friendship and thinks they could be a great 'power couple' in showbiz. It's all a bit embarrassing for him."
A friend of Contostavlos's added: "Tulisa enjoyed spending time with Mark and they did hit it off. But despite Mark staying over nothing more happened and things didn't go too far. She's not that sort of girl.
"Tulisa definitely doesn't intend for things to go further right now and she's very annoyed that Mark has been telling people about what happened."
Contostavlos previously denied the pair were dating when rumours first surfaced in November last year.
She split from fellow N-Dubz star Fazer in January, while Wright broke off his engagement to TOWIE's Lauren Goodger last August.
Watch Tulisa Contostavlos perform with Little Mix on The X Factor below: