Wilson, the former San Francisco Giants closer, went 2-1 with a 0.66 ERA in 18 games as a setup man to Dodgers closer Kenley Jansen this past season after coming back from his second Tommy John surgery.
Sources said Wilson has made it clear to the Dodgers that he's willing to return to the team as a setup man in 2014, with an opportunity to take over as closer if Jansen falters or gets hurt.
A strong and deep bullpen was a significant factor in the Dodgers' run to the National League West title in 2013. Los Angeles' bullpen went 30-24 with an aggregate 3.49 ERA, while ranking seventh in the league in strikeouts (451) and fourth in batting average against (.240).
The Detroit Tigers, Seattle Mariners and Colorado Rockies were among the other teams that expressed interest in Wilson during his free-agent search. The New York Yankees, another potential suitor, fell by the wayside once it became clear that Wilson would not be willing to shave his trademark beard in accordance with the club's facial hair policy.
The Dodgers signed Wilson to a $1 million contract on July 30 after scouting several of his workouts. He was promoted to the majors on Aug. 19.
The Dodgers did not tender an offer to former setup man Ronald Belisario on Monday night, resulting in him becoming a free agent. That left the Dodgers with just three experienced relievers who were healthy last season: Jansen, Brandon League and Paco Rodriguez.
The Dodgers also are believed to be in talks to re-sign J.P. Howell, who was the team's primary left-handed reliever by the end of the season.
Mark Saxon of ESPNLosAngeles.com contributed to this report.