Okajima, 36, was an effective force for Boston in his first few seasons after coming to the Majors, but fell out of favor with the Red Sox and spent most of this season at Triple-A Pawtucket.
Though he has also had success against right-handed batters, Yankees general manager Brian Cashman said that the club is considering Okajima as a left-handed specialist.
"He's somebody that definitely can get left-handers out," Cashman said. "We'll see what it looks like when we get to Spring Training."
Okajima was limited to just seven big league outings in 2011, all of them coming in April and May. Okajima was 1-0 with a 4.32 ERA in 8 1/3 innings.
The Red Sox did not recall Okajima when rosters expanded in September, despite a 2.29 ERA in 34 appearances at Triple-A, spanning 51 innings.
Okajima came to the Major Leagues in 2007 after pitching with the Yomiuri Giants and Hokkaido Nippon Ham Fighters in Japan. He compiled a big league record of 17-8 with six saves and a 3.11 ERA in 261 appearances with Boston, holding left-handed batters to a .218 batting average.
The Yankees have been looking for supplemental left-handed help after going most of 2011 with Boone Logan as their lone southpaw reliever.
"We're just kind of casting a wide net to see if we can nail something in the spring," Cashman said. "Some years you have better success at that than others."
New York also traded up to acquire another Red Sox left-hander in the Rule 5 Draft earlier this month, acquiring 22-year-old Cesar Cabral from the Royals in exchange for cash considerations.
In other updates, Cashman said that he remains in contact with the representatives for infielder Eric Chavez and outfielder Andruw Jones but that there is nothing new to report with their respective situations.
In Chavez's case, the Yankees are waiting to see what happens with 29-year-old Japanese infielder Hiroyuki Nakajima, whom they acquired the rights to negotiate with in early December from the Seibu Lions for $2.5 million.
New York has until Jan. 6 to reach an agreement with Nakajima, who can play shortstop as well as second and third bases. The Yankees also have Eduardo Nunez and Brandon Laird in line as potential backup infielders.
"Until the Nakajima thing declares itself either way, I'm really not in a position to pursue anything else, because he very well may be here," Cashman said. "If he is, that's an exclamation point to what I have. If he isn't, potential discussions with other players can continue."