Ryan, the 49-year-old star of films such as "When Harry Met Sally," and Mellencamp, known for hits such as "Hurts So Good," have not commented on the report by People magazine, which said the two spent time together on Martha's Vineyard in New England and in New York City in recent days.
It quoted a source close to the actress as saying that she and John have been dating for about seven weeks.
Mellencamp and his wife, a 41-year-old former model, Elaine, wed in 1992 and have two sons.
They said in a statement last week that they would continue to raise their children in Indiana but would "call it a day as a couple."
John also has three other daughters from two previous marriages.
Ryan was married to actor Dennis Quaid between 1991 and 2001. They have an 18-year-old son named Henry and Ryan also has a 6-year-old daughter, Daisy True, whom she adopted from China.
In recent years, She has starred in movies such as "The Women" and "Serious Moonlight." She also stars in the film "Lives of the Saints," which stars John Lithgow and 50 Cent and is due for release later this year.
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