The New York Daily News reported Friday, citing TicketNews.com, the former Beatles star has agreed to play the New York ballpark's first show July 17 with an additional performance scheduled for the next day.
TicketNews.com said a third McCartney show could potentially be added with a July 21 date mentioned as a possibility.
The reported performances by McCartney would take place while the Mets are idle for the All-Star Game break and then on the road July 12-27.
The Web site said it obtained its information regarding the possible McCartney performances from unidentified touring industry executives.
The Daily News said McCartney appeared as a guest star for performances by singer Billy Joel that marked the last shows at Shea Stadium, the Mets' former home stadium.