"I maybe want to play a year at 40, maybe 41," he told Mike Reiss of ESPN.com.
The Patriots picked up Harrison on waivers in December from Pittsburgh, where he played in six games for the Steelers this season. Harrison has been solid as a situational edge rusher, making 11 tackles in three games, including two in the playoffs.
Harrison will be a free agent this offseason.
Harrison, who spent nearly his entire career with the Steelers -- save for this stint in New England and the 2013 season with the Cincinnati Bengals -- has 84.5 career sacks.