The two-year term -- something that was of utmost importance to the 36-year-old Ortiz -- already has been agreed upon, the source said Tuesday, but the sides are still haggling on compensation.
Ortiz is believed to be seeking a total of $25 million. The Red Sox are in that neighborhood but hope to sign him for a few million less, according to the source, who noted the monetary negotiations are not expected to get in the way of the deal's completion.
A Red Sox source cautioned there was still some work to be done before the deal is finalized.
"As I said, we want to have David back," general manager Ben Cherington said Tuesday. "We've had good, amicable dialogue. I talked to Fernando (Cuza, Ortiz's agent) yesterday. We'll continue to keep talking. Our hope is to get something done. I'm sure we'll talk again this week sometime."
The Red Sox hope to announce the extension as soon as Friday, the first off day of the World Series. The league frowns upon teams announcing news on days of World Series games.
Representatives of the team -- including Cherington and newly hired manager John Farrell -- talked with Ortiz on Tuesday at Fenway Park, where he was working out.
Ortiz, who made $14.575 million on a one-year deal struck on the same day his arbitration case was scheduled to be held this past February, missed 71 of Boston's final 72 games because of a right Achilles strain. He told ESPNBoston.com on Sunday that he's feeling much better and will begin his normal offseason workout regimen soon.
"I'm 36, and I know what I'm capable to do," Ortiz said Sunday. "I know what's fair and I know guys my age aren't going to get three-, four- or five-year deals anymore, so I want to play two more, and if things go good, I'll continue to play."
The Dominican-born slugger was having one of the best years of his career before the injury, hitting .318 with 23 homers, 60 RBIs and a 1.026 OPS in 90 games.
He's the longest-tenured player on the Red Sox, having played in Boston over the past 10 seasons.