The Marlins have not commented on the report.
Mattingly has a 446-363 record in five years as Dodgers manager and has led the club to three straight National League West division titles. Mattingly's clubs have finished with five straight winning records.
The Marlins finished 71-91 this season under managers Mike Redmond (16-22) and Dan Jennings (55-69). Redmond was dismissed in May, and Jennings, the team's general manager, handled the managing duties for the rest of the season.
Spencer Fordin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.