The Canadian supermodel and Hard Rock Cafe founder Peter Morton are said to have called time on their four-year romance a couple of months ago after a series of rows about where they should live.
A source said: "Peter is very settled in Malibu and loves Los Angeles, while Linda liked to spend time in Canada and with her friends in New York. Like all supermodels, she is high-maintenance and likes to be treated like a princess."
Sources claim the couple got engaged last year, although his family weren`t too impressed with the news.
One told the New York Post newspaper: "Some members of Peter`s family were not too fond of her, and were dismayed when she appeared around last Thanksgiving with a large diamond ring on her finger. But the marriage never happened."
Linda, 45, and 64-year-old Peter started dating in 2006 when Linda was pregnant with her son, Augustin, although she has never revealed who the father is.
A spokesperson for Linda - who has previously dated French soccer star Fabian Barthez and actor Kyle MacLachlan - refused to comment on the reports.