Is a romance between Katy Perry and Robert Pattinson really heating up?

According to sources, the British actor wants the Teenage Dream singer to meet his parents.

"Rob confessed that he was falling for her after their date night at the Bjork concert, and it's left Katy in turmoil," a source reportedly told

The two were seen hanging out together at the Hollywood Palladium in Los Angeles on June 8 enjoying the Bjork concert. Pattinson and Perry also reportedly left separately but spent the whole time hanging out inside the venue.

"He's planning a trip to the U.K. and wants Katy to go with him to meet his parents," the source also added. 

Reports from early June also claim that Perry's mother and father have already met Pattinson when he visited the singer in her Santa Barbara, Calif., hometown. Rumors began swirling because the two stars have been spotted hanging out a few times since Pattinson's breakup from Twilight co-star Kristen Stewart in April. Perry and her ex-boyfriend, singer John Mayer, also called it quits a month later in March.

Perry hasn't confirmed the relationship with Pattinson. In fact, she insisted recently that she's single.

"I'm not in a relationship, I'm just on my own -- I am myself in my own bed," she told Vogue in the July 2013 issue. "I have to be happy being alone, and I am happy." 

She also opened up about her relationship with Mayer and said that although their love affair is over, she is still "madly in love with him." She also added that he has a "beautiful mind," yet he's a "tortured soul."

The Vogue cover girl said, however, that she's not giving up on love just yet.

"I believe that I will be loved again, in the right way," she said. "I know I'm worth it."