The 38-year-old designated hitter shared the news with reporters at his annual charity golf tournament in the Dominican Republic.
"My lawyers are talking with the Red Sox to see if we can get another year, and we'll see what happens later," Ortiz said to Dionisio Soldevila of ESPNDeportes.com in Punta Cana, Dominican Republic.
"Maybe I'll play another year or two more years. I'm at a stage where I'll play depending on how I feel physically. Looking at Cano's deal and the rest of the boys that came only yesterday to the big leagues, signing those contracts, one says, 'that's why we're here.'"
Red Sox general manager Ben Cherington, talking to reporters on a conference call to announce Mike Napoli's deal, said that conversation has yet to take place.
"I can say I have incredible respect for David," Cherington said. "As I've said before and I'll reiterate, our hope certainly is that he finish his career in a Red Sox uniform. At some point there will be a conversation about that, and I don't know when that will be. It's early December, there are still things we are looking to do to improve the team. The door will always be open to David. I'm sure at the appropriate time there will be an opportunity to have a conversation."
Ortiz signed a two-year contract prior to last season that included a $4 million incentive for 2014 that he reached by spending 20 days or fewer on the disabled list with an Achilles injury. He spent 15 days on the DL with the injury to start last season and was healthy the rest of the way, thus increasing his 2014 salary from $11 million to $15 million.
He is coming off one of the best postseasons by any hitter in recent history, hitting .353 with five homers and 13 RBIs in 16 games in leading the Red Sox to their third championship in 10 years.
He also sported a .500 on-base percentage and a 1.206 OPS in the playoffs. In six games against the St. Louis Cardinals in the World Series, Ortiz hit .688 with two homers, six RBIs and a whopping 1.94 OPS. He reached base in 19 of 25 plate appearances.
In the regular season, his 11th with Boston, Ortiz hit .309 with 30 homers and 103 RBIs. He recently won his sixth Silver Slugger award and was named the winner of the Edgar Martinez Award as the best designated hitter in baseball for the seventh time.