The one-year deal is worth $6.275 million, according to a source who spoke on condition of anonymity.
Billingsley, who went 12-11 last season, took big steps with his consistency in 2010, dropping his ERA to 3.57 from 4.03 in 2009. Last winter, he avoided arbitration by agreeing to a one-year, $3.85 million contract for 2010.
In each case, the gap seemed small enough that the sides would appear likely to reach an agreement well in advance of going to an arbitration hearing in February.
Kuo, who made $975,000 last season, is seeking $3.075 million through the arbitration process, while the club filed at $2.55 million. Loney, who made $3.1 million last year, is asking for $5.25 million while the club filed at $4.7 million.
If either player goes to a hearing, after hearing each side state its case, a three-person arbitration panel would be forced to choose one of those two figures, with no wiggle room in between. Until such a hearing, though, the two sides are free to reach an agreement at any figure, and the sides often settle at the midpoint.
The mathematical midpoint for Kuo is $2,812,500. For Loney, it is $4,975,000.
Only two players -- pitchers Eric Gagne in 2004 and Joe Beimel in 2007 -- have taken the Dodgers all the way to an arbitration hearing in the 10 years that assistant general manager Kim Ng has been handling cases for the club. Both of those players lost their cases.
Meanwhile, Gabe Kapler, who returned in 2008 from a year-long retirement to a major-league playing career, has signed a minor-league contract with the Dodgers.
Last season, the 35-year-old outfielder had a .288 on-base percentage and .290 slugging percentage in 140 plate appearances with Tampa Bay.
After retiring following the 2006 season, Kapler managed the Greenville Drive of the Class A South Atlantic League to a 58-81 record. He then returned to the playing field in 2008 with the Milwaukee Brewers, for whom he had one of his best seasons: an .838 OPS in 245 plate appearances.
The Dodgers have already made several signings this winter to try to fill out their outfield alongside Andre Ethier and Matt Kemp, agreeing to terms with Marcus Thames, Jay Gibbons and Tony Gwynn Jr. In-house options Xavier Paul and Jamie Hoffmann, among others, will also return.
Kapler went to Taft High School in Woodland Hills, Calif. Detroit selected him out of Moorpark College in the 57th round of the 1995 amateur draft.
ESPNLosAngeles.com's Tony Jackson and Jon Weisman contributed to this report.