The 'Promise This' singer and the Dancing With The Stars pro have seen their close relationship pushed to breaking point by Cole's "negative" attitude during her X Factor USA troubles, the Sunday Mirror claims.
"It's sad - but it was just not working out," Hough's stepfather Aaron Nelson stated. "Derek just wants to move on with his life."
Hough is also believed to have shared his concerns about Cole with friends, telling them: "I love that girl with all my heart, but I just can't do it any more. I have done everything I can to pick Cheryl up. But every time I am with her she refuses to leave her room for days and days.
"It's not healthy behaviour and doesn't make for a healthy relationship. It's tough but I have to leave Cheryl and get on with my life."
Sources connected to the pair further report that Cole is now considering a reunion with ex-husband Ashley, with whom she has always shared a "spark".
They said: "Everyone knew Derek and Cheryl would drift apart eventually. Derek has been wonderful support for her during the last year, but there was a real lack of spark between them.
"With Ashley it is so different. He is still the one person who can make Cheryl smile when she feels down. The truth is she's still in love with Ashley.
"He has been there for her over the last few days and is desperate for them to try again. Cheryl is certain in her own mind that he's turned over a new leaf."
Cole is rumoured to have been hired back to the X Factor USA panel after apparently being replaced by Nicole Scherzinger last week.
Executives on the Fox show allegedly ordered the Girls Aloud singer to dump Hough last month.