Yankees general manager Brian Cashman met with Youkilis' agent, Joe Bick, at least twice during the Winter Meetings, and there is a sense that Youkilis would be willing to consider a one-year deal if the salary was substantial enough.
New York's offer nearly matches Youkilis' $12.25 million salary in 2012, when he batted a combined .235 with 19 home runs and 60 RBIs in 122 games for Boston and the White Sox, having been traded to Chicago in late June.
Cashman said he "wouldn't say" if the Yanks had made an offer to Youkilis, adding, "I'm not in a position to say offers [or] non-offers." The terms of the offer were first reported by MLB.com.
The Yankees are searching for third-base help with Alex Rodriguez headed for left hip surgery, which could potentially keep him out of action until June or July.
The Indians are believed to be New York's prime competition for Youkilis, who turns 34 in March, and could be willing to offer Youkilis a two-year pact to play under former Boston manager Terry Francona.
Youkilis is a career .283 hitter in 1,033 big league games, hitting 148 home runs and collecting 610 RBIs beginning with his callup to Boston in 2004.
New York's offer is believed to be Cashman's first solid one to plug the third-base vacancy with a free agent, though the team has also met with the agent for Mark Reynolds and may look at him as a backup plan if Youkilis goes elsewhere.
Cashman said that although the Yanks had interest in Eric Chavez and Jeff Keppinger, he did not make either player an offer before they came to terms with the D-backs and White Sox, respectively, on Wednesday.
The Yankees do not believe they have an in-house candidate to fill third base for an extended period. Cashman has said that the club does not view Eduardo Nunez as anything but a shortstop, and Jayson Nix is looked at more in a utility role.
Though Minor Leaguers David Adams and Ronnier Mustelier have seen some time at third base, they are not thought to be serious options at this time.
"The bottom line is, we've got some work we're trying to accomplish and we'll see where it takes us," Cashman said.