Marmol, 30, was an All-Star in 2008, but his best season was 2010, when he finished a
The hard-throwing right-hander has averaged more than a strikeout per inning the last seven seasons, but his record was 2-4 with a 5.86 earned-run average and he had lost his job as the Cubs' closer when he was designated for assignment last week.
Marmol is in the final year of a three-year contract and is owed about $5 million.
It is not known what the Dodgers would send to the Cubs in return, or if Marmol would be part of a multiple-player package heading to Los Angeles.
If the Dodgers manage to acquire him, he would probably not go straight onto the major league roster. Marmol hasn't pitched since June 20, so he would probably first pitch in the minor leagues or at the Dodgers' spring-training complex.
Last season, the Dodgers acquired and turned around another struggling former closer,
For the Dodgers, League saved six games and had a 2.30 ERA in 28 appearances, which he parlayed into a three-year, $22.5-million deal with the Dodgers over the winter.
However, League has reverted to his Mariners form from last season, which again cost him the closer's role. League is 3-3 with a 5.83 ERA this season.