Renée Zellweger and Bradley Cooper
Jackson Lee/Splash News Online
08/18/2009 at 06:00 PM EDT
The romance between Renée Zellweger
and Bradley Cooper appears to be heating up, but the pair aren't ready for the spotlight just yet.
"They get along really well and just kinda click," a source tells PEOPLE in the upcoming issue. "Bradley likes the speed of everything. He likes that Reneé is low-key."
The pair, who costar in the upcoming thriller Case 39
, recently spent time in Spain
together, then returned to the States, where they each went their separate ways – briefly.
On Saturday, Zellweger attended the premiere of her new movie My One and Only
in Wainscott, N.Y., while Cooper was a guest at Alyssa Milano's wedding
in New Jersey that same evening.
But the cozy costars soon met up again. Sunday night, they attended a private party together in New York City, then were spotted at a Starbucks in Philadelphia on Monday.
As for why Cooper didn't come to Zellweger's screening and she didn't accompany him to the wedding, the source tells PEOPLE: "They're not ready for red carpets. They don't want to be public just yet."
With reporting by JENNIFER GARCIA