Furcal is hitting just .197 with a .272 on-base-percentage in 37 games in an injury-plagued season this year. But he has shown signs of recovery lately, hitting .303 and driving in five runs in his last nine games.
The veteran shortstop, a two-time all-star with a career .283 batting average, has to approve the deal for it to become final.
In return, the Dodgers received 24-year-old Alex Castellanos, who had belted 19 home runs and was hitting .319 in 93 games for Class AA Springfield this season.
"We feel that Furcal will give us added veteran experience when it comes to a pennant race," Cardinals General Manager John Mozeliak said. "Rafael has been an excellent top of the order hitter and he brings plenty of athleticism and defense."
The Cardinals entered Sunday's play 1 1/2 games behind Milwaukee atop the National League Central.