The 68-year-old and his Welsh wife - who went to rehab in 2011 to deal with bipolar II disorder, just a short time after her husband battled throat cancer - want to put the troubles of the past years behind them and go to Bermuda to say their vows once more, reported Daily Star.
"They want to put a few difficult years behind them. It will be a private affair in Bermuda," a source said.
Jones, who has children Dylan, 12, and Carys, nine, with Michael, may use the opportunity to get her family together as she recently said she missed all of her family in Wales as she has spent so much time in the US.
"It's really hard for me because I've been out of Wales longer than I ever lived there. My family is so close that I really miss just being able to say to my mam or my friends, 'Just come on over for a cup of tea and we'll talk through stuff'. And I miss my friends from the dancing school that I'm still in touch with. I miss the immediacy."