The deal includes the possibility of bonuses that could raise Napoli's 2013 income to $13 million, according to the person, who spoke on condition of anonymity Thursday because the agreement was not yet final. That amount is what Napoli would have earned this season in the $39 million, three-year deal agreed to at last month's winter meetings, subject to a successful physical.
The Red Sox became concerned about Napoli's hip, and that agreement was never announced. The person said language in the new deal still had to be finalized and Napoli's deal likely will be announced next week.
A 31-year-old catcher and first baseman, Napoli hit .227 with 24 homers and 56 RBIs last year as he became a first-time All-Star. He is a .306 career hitter at Fenway Park, with seven homers and 17 RBIs.
Also Thursday, the Red Sox and catcher Jarrod Saltalamacchia agreed to a $4.5 million, one-year deal, a raise of $2 million.
Saltalamacchia hit .222 with 25 home runs and 59 RBIs last season, when he became the first catcher to lead the Red Sox in home runs since Carlton Fisk hit 26 in 1973 and again in 1977.
Acquired by Boston from Texas on July 31, 2010, Saltalamacchia is a switch-hitter who set a career high for games last year with 121. His deal, which is not guaranteed, avoided salary arbitration.
Eight Red Sox remain in arbitration: outfielder Jacoby Ellsbury; right-handers Alfredo Aceves, Andrew Bailey, Daniel Bard and Joel Hanrahan; and left-handers Craig Breslow, Andrew Miller and Franklin Morales.