The rocker was inspired to pen Been Caught Cheating by reports of the Back to Black hitmaker's tumultuous love life and approached her about the possibility of recording the tune.
Winehouse, who was dating filmmaker Reg Traviss at the time of her death, passed away before she had heard the track, so the band has featured it on new album, Graffiti on the Train.
Jones tells Britain's Daily Star newspaper, "I read an article about Amy's love life and the line 'Been caught cheating' came to me. I'd said hello to Amy at festivals and then I bumped into her at a record company party where she was with her fella Reg Traviss. I've met Reg a couple of times since Amy died; he's a lovely guy.
"We got talking about songwriting and Amy was up for me sending her this song, but I never got round to it. I thought it was too bluesy for Stereophonics to play but it's come out really raw and tough."
Winehouse, whose whirlwind romance and subsequent divorce from Blake Fielder-Civil hit headlines, was found dead in her London home after a booze binge.