"Orlando and Katy are spending more and more time together," a source tells PEOPLE
Credit: Frazer Harrison/BAFTA LA/Getty; Hubert Boesl/DPA/Zuma

There’s nothing “Hot n Cold” about these two – Katy Perry and Orlando Bloom‘s relationship is revving up.

“Orlando and Katy are spending more and more time together,” a source says in the new issue of PEOPLE, adding the pair doesn’t shy away from PDA in public. “They are introducing each other to friends [and] they look very happy together.”

Indeed, on Thursday, Perry, 31, accompanied Bloom, 39, to his manager’s birthday celebration, where they hung with his pals Jennifer Aniston and Jason Bateman.

For more on Katy Perry and Orlando Bloom, pick up this week’s issue of PEOPLE, on newsstands Friday.

Then two days later, the singer joined Bloom and his son (with ex Miranda Kerr) Flynn, 5, at a birthday party for Robert Downey Jr.‘s son Exton.

“They were laughing, playing music and joking around with Flynn,” an insider told PEOPLE at the time. “They stayed at the party for hours. Katy looked very comfortable at the kids party. She seemed very happy to spend the day with Orlando.”

Perry and Bloom ignited whispers regarding their relationship at the Golden Globes last month, where they gabbed for half an hour and even shared a drink.

The actor was recently linked to stylist Chloe Bartoli and Brazilian model Luisa Moraes, while Perry spent time with off-again ex John Mayer over New Year’s.