He can accept the offer by Nov. 10 and sign for next season or he can decline and remain a free agent.
The move on Monday ensures the Dodgers of receiving a supplemental draft pick if Ramirez signs with another team. The club signing that player loses its first-round pick in the amateur draft, unless that pick is among the top 10, in which case the club signing that player loses its next-highest pick.
Ramirez hit .283 with 13 homers and 71 RBI while missing 34 games with various ailments. He turns 31 in December.
Pitcher Scott Elbert elected to become a free agent.
In other moves, the Dodgers claimed infielder Ryan Jackson from San Diego. He has a .268 career batting average with 27 homers and 203 RBI in 576 games over six minor league seasons.
The 26-year-old made his major league debut with St. Louis in 2012, and appeared in 20 games in 2012-13. Jackson was originally selected by the Cardinals in the fifth round of the 2009 draft out of Miami.