DJ AM and Nicole Richie Reunite  3/9/06

Nicole Richie and Adam 'DJ AM' Goldstein have rekindled their romance - but their engagement is still on hold.

The couple stayed in contact after breaking up in December (05) and have been seen regularly around Los Angeles holding hands and kissing.

A source tells American publication US Weekly, "Nicole convinced him to give her a second chance, but they're not engaged.

"She asked if she could put her ring back on and he said no."

After the intense media scrutiny after their break-up The Simple Life star vowed not to discuss her personal relationships with the media again.

The couple, who dated for nearly two years before separating, are taking things slowly.

The source adds, 'The miss each other and want to try it again."