"My agent and them, they're talking right now to see if we can get another year," Ortiz said Friday. "Hopefully everything goes well. Right now, I am very happy with the way things went down this year."
General manager Ben Cherington said that the club would likely sit down with Ortiz and his representatives once the time was appropriate.
On a day Mike Napoli talked about his a new two-year deal with the Sox, Cherington didn't want to steal the first baseman's thunder by talking too much about Ortiz.
"Well, as you know, as a policy, we prefer not to talk about our conversations with players," Cherington said. "Out of respect to David, it's hard for me to respond, because I wasn't there and don't know exactly what he said. What I can say is that we have incredible respect for David, and as I've said before and I'll reiterate, our hope certainly is that he finishes his career in a Red Sox uniform.
"So at some point there will be a conversation about that. I don't know when that will be. It's early December and there are still things we're looking to do this offseason, working on different ways to improve the team. The door will always be open to David, and I'm sure at the appropriate time there will be an appropriate time to have the conversation -- and I hope he's in a Red Sox uniform the rest of his career."
Ortiz signed a two-year deal after the 2012 season.
The lefty slugger had a strong 2013 season, hitting .309 with 30 homes and a slash line of .395/.564/.959.
In the postseason, Ortiz took his game to another level, hitting a monumental grand slam in Game 2 of the American League Championship Series and then being named the World Series Most Valuable Player.
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.