Cleveland has yet to confirm the signing, which was reported via Twitter by Dionisio Soldevila of the Associated Press.
Lugo would become the 20th non-roster invitee (12 having signed Minor League deals) of the offseason for the Indians. Other infielders added this winter include Jose Lopez, Andy LaRoche and Gregorio Petit.
Indians manager Manny Acta knows Lugo from their days in the Astros organization. Acta was actually Lugo's first manager when the shortstop broke into the Minors as a 19-year-old infielder with Class A Auburn in 1995.
In parts of 12 Major League seasons -- including stops with the Astros, Rays, Dodgers, Red Sox, Cardinals, Orioles and Braves -- Lugo has hit .269 over 1,352 career games. Last year, he signed a Minor League contract with Atlanta in May, but was ultimately released in September.
Lugo hit .231 (12-for-52) in 13 games for Triple-A Gwinnett and .136 (6-for-44) in 22 games with the Braves during the 2011 season. The 36-year-old infielder hits right-handed and has experience at second base, shortstop, third base and in the outfield.