The 'Promise This' singer first met Paltrow when the Oscar winner's husband Chris Martin accompanied Girls Aloud on a 2009 tour, but The Mail On Sunday claims that their friendship has strengthened while Cole attempts to launch her career stateside.
The celebrity pair are believed to have reunited while they were both staying at Hollywood's Sunset Marquis Hotel, Cole's American base as she awaits news of her possible recruitment to the X Factor USA judging panel.
A source revealed: "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".
Cole has reportedly sunk into a depression and adopted a junk food diet during her time in the US. She is also believed to have started contacting ex-husband Ashley for support.