The `City of Angels` actress was spotted together with the -Jack and Diane- rocker in New York, and friends say they have been seeing each other quietly for several weeks, less than a week after John announced his split from his wife of 20 years, former model Elaine Irwin.
Meg - who moved to New York last year - has been seen with John, 59, in the Martha`s Vineyard Island off the coast of New England, and in New York - where they are said to be regular customers of the Gourmet Garage grocery store.
A source linked to the store told People.com: "She usually comes in by herself or with her daughter. I thought that was her husband because they seemed for comfortable and familiar with each other, just like an old married couple."
John has been married three times and has five children, including two sons with Elaine. Following his shock split from his wife, he spent a low key New Year at his home in South Carolina.
Meg, 49, has been married once, to actor Dennis Quaid, whom she separated from in 2000, after 10 years of marriage. She has been largely single since, apart from a brief fling with the actor Russell Crowe around the same time her marriage ended.
Meg has one son with Dennis, Jack Henry, who is 18 and she also adopted a daughter, Daisy True, six, from China.