The 'Back To Black' singer dated Clare, who was working as a chef in her local pub, prior to her marriage to Blake Fielder-Civil. He was signed to Island Records last year.
However, The Sun reports that Winehouse is now worried that her ex will write material about their romance.
"Amy is petrified that Alex will reveal everything about their relationship in his songs," a source said. "The worst thing is the music is really good so she knows he is heading for the big time."
The paper claims, that following the couple's split, Clare wrote on MySpace: "After turning up at 3am at The Hawley Arms I saw the ex with her ex and I saw red mist. I was shaking like a leaf and decided to get leathered while she sat there inebriated and on the lap of her ex.
"I'm skint, heartbroken and homeless. Bad luck comes in threes, as the old saying goes, but s**t, what's a man to do?"
Clare, whose real name is Alexander G. Muertos, will release single 'Too Close' next month.
Earlier this month, Winehouse was booed off stage during a gig in Dubai.
> Winehouse to unveil new songs on tour