MLB.com was the first to report the Yankees made an offer to Youkilis.
If he signs with the Yankees, Youkilis would step in at third base for Alex Rodriguez, who is likely to miss much of the first half of next season because of second hip surgery that is expected to take place in January.
It has been a quiet offseason for the usually free-spending Yankees, who have concentrated on re-signing their own free agents. Closer Mariano Rivera and pitchers Andy Pettitte and Hiroki Kuroda both have inked new deals. Catcher Russell Martin signed a two-year deal with the Pittsburgh Pirates.
On the current roster, Jayson Nix and Eduardo Nunez are possibilities to play on the left side of the New York infield. But Yankees general manager Brian Cashman said he didn't look at Nunez as a third baseman.
A three-time All-Star known for his ability to get on base, Youkilis has seen his numbers decline in recent seasons. His batting average last season was the lowest of his nine-year career.
Youkilis, 33, also is an above-average defensive player, winning a Gold Glove in 2007. In addition to third base, he also the ability to play first base.