07/19/2012 12:19 pm ET

Amber Heard Reportedly Freaked Out By Attention Over Johnny Depp

Last month it was reported that actress Amber Heard broke up with her girlfriend, artist-photographer Tasya van Ree, only to hook up with her recently single "The Rum Diary" co-star Johnny Depp.

Though they do make a beautiful couple, RadarOnline reports that things have cooled down between the former co-stars.

“Johnny and Amber were definitely involved,” a source told the website, of the couple who met on set while Depp was still involved with his partner of 14 years, Vanessa Paradis, and Heard was still with Ree.

The source didn't suggest that either cheated on their former partner, but said that the two actors "definitely had chemistry that carried over from the set," and they just happened to find themselves single at the right time.

The source tells RadarOnline that Depp and Heard were hooking up for months -- way before he ever made his split with Paradis public.

"They did a really good job of keeping their relationship on the down low for a while, especially since many people assumed that Amber was only into girls.”

But there's a reason that so many celebrity couples try to keep their relationships private, as Heard allegedly freaked out when it was reported she was seeing Depp.

"She prides herself on being free-thinking and independent -- not some homewrecker trying to sleep her way to the top. As soon as the media started publicizing the romance, she told Johnny that she needed some space," explained the source.

Depp and Paradis' relationship was rumored to be on the rocks for months, and after the actor finally announced their breakup, there were reports about how much of it was due to the fact that Depp had become "bored senseless."

Depp's alleged boredom makes his reported relationship with the gorgeous 26-year-old make all the more sense. But even if Depp was looking for something a little more exciting, sources say Heard wants things to be more low-key.

"She really likes Johnny, but she doesn’t like the drama. She isn’t really sure what is going to happen with them, but just wants the attention to cool down before anything progresses," the source told the website.