Coughlin has guided the Giants to two Super Bowl wins over the New England Patriots in the 2007 and 2011 seasons, but his team has struggled in the past two years.
The 67-year-old's contract ends after the 2015 campaign, but Mara has admitted that the head coach will not be the one who chooses when to end his affiliation with the club.
"Does anybody ever earn that right? That's just not the way this business is in this day and age," Mara told the New York Post.
"Let's hope that it goes that way, but we haven't even had that discussion yet. ... We're just looking forward to the next couple of seasons."
The Giants finished with a 7-9 record in the 2013 season.