The X-Factor judge first got to know Gwyneth after meeting her husband Chris Martin during a Girls Aloud tour in 2009, and their friendship is said to have strengthened since she moved Stateside.
According to The Mail On Sunday, both were staying at Hollywood's Sunset Marquis Hotel, where Paltrow gave Cole a shoulder to cry on as she waits to find out if she will be offered a role on the US X-Factor.
A source told the newspaper: 'Gwyneth has had ups and downs in her marriage and Cheryl can relate to that so she's offered lots of advice to her. And Cheryl's been worrying that her US career won't take off so Gwyneth's been putting her in touch with the right people'.