(AP)

Chris Martin is denying cheating on wife Gwyneth Paltrow after a story surfaced that he was canoodling with actress Kate Bosworth.

Star magazine reported that the Coldplay lead singer was spotted making out with Bosworth, but a source close to the couple backs Chris, adding that while the couple has issues, Kate Bosworth is not one of them.

"Chris did not hook up with Kate in public or private," the insider tells Fox411. "Chris has enough to deal with his work, his children and Gwyneth. He is not adding an affair with another A-lister to his list of things to do."

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The source says Paltrow is also brushing off the story as best she can.

"Chris pretty much laughed off the accusations and even Gwyneth was fairly unaffected," says the source. "She trusts Chris would not cheat on her in such a blatant, public manner."

The source says Gwyneth and Chris have enough problems without adding this to the mix.

"Gwyneth and Chris are always on a different page, but he is not stupid," says the pal. "Chris wishes that Gwyneth would loosen up and be a little less uptight about everything, but he would never hurt his family this way. He actually loves to mock Gwyneth and all her projects. That's a bigger problem for them than the rumors."

The source says Chris likes to tease her to the point that now he's doing it in front of other people, even when he's visiting her on a movie set.

"People pick up on it and some play along with him because he's just so cool. Guys that work for Gwyneth always want to be buds with Chris and it crosses a line for her when he gets them to start goading her, too," says the insider. "It's one of those couple problems."

And apparently Paltrow has had just about enough of it!

"Gwyneth has recently pulled him aside and told her to stop mocking her around others, fairly pointing out that random people are 'not our friends'."

The one thing the couple does agree on is their children, Apple, 5, and Moses, 3.

"Gwyneth is a protective and loving mother and that is something that Chris absolutely cherishes about their relationship. He likes to tease, but in the end, he cares about her very much."