The right-handed Turner, 29, hit .280/.319/.395 with 13 doubles and two home runs in 86 games. He was non-tendered by the Mets on Dec. 2, making him a free agent.
In parts of five major league seasons with the Orioles and Mets Turner, who graduated from Mayfair High School in Lakewood and played college ball at Cal State Fullerton, has hit .260/.323/.361, a 92 OPS+, with 57 doubles in eight home runs. He has played 301 of his 318 career major league games with New York.
General manager Ned Colletti on Saturday said the Dodgers were finalizing a minor league deal with someone, though he wouldn't name names.
"We're working on one more infielder that hopefully we're going to sign in the next five days, a utility type that has some versatility to him," Colletti said.
In his career Turner has started 88 games at second base, 50 games at third base, 21 games at shortstop and 17 more at first base. With the Mets in 2013, Turner played 127⅓ innings at third, 115⅓ innings at shortstop, 87⅔ innings at first base and 46 innings at second base. He also played his first career game in the outfield last year, though that consisted of all of one inning in left field.
Turner rates roughly average to below average around the infield, but at second base he comes in at a woeful -18 runs in defensive runs saved by Baseball Info Solutions and -13.5 runs in UZR, though his only real extended time at the position came in 2011.
Turner will make $1 million plus incentives if he makes the team, per Jon Heyman of CBS Sports.
With newcomer Alex Guerrero having a tenuous hold on the starting second base job, the Dodgers' bench is a fluid situation. But Turner will have a good shot at winning a spot on the roster, fighting with Dee Gordon, Justin Sellers, Chone Figgins and Brendan Harris for likely two open spots.
Dodgers position players report to spring training at Camelback Ranch in Arizona on Thursday, Feb. 13.