Kershaw, who will be eligible for free agency after the 2014 season, was one of 146 players to file for salary arbitration Tuesday.
The arbitration process likely has accelerated the Dodgers' negotiations with Kershaw, who figures to command one of the most lucrative contracts in baseball history.
The Dodgers offered Kershaw a deal in the range of $300 million this past season, a source with knowledge of the talks told Olney in October. Although Kershaw initially was uncertain about committing to a deal, the sides were confident that a long-term contract would be completed at some point in the offseason, according to the source.
Kershaw, 25, also could land a record-breaking deal for an arbitration-eligible player if he doesn't agree to a long-term contract with the Dodgers.
Fox Sports reported earlier Wednesday that the Dodgers want the deal completed by Friday. The new contract would include an opt-out clause that would allow Kershaw to become a free agent after five years, according to Fox Sports.
Kershaw, who has won two NL Cy Young Awards in the past three seasons and three straight ERA titles, made $11 million last season.
The Dodgers haven't had a case reach arbitration since 2007.
Kershaw went 16-9 with a 1.83 ERA and 232 strikeouts last season, his sixth with the Dodgers. The left-hander has a 2.60 career ERA and recorded at least 212 strikeouts in each of the past four seasons.
ESPNLosAngeles.com's Mark Saxon and The Associated Press contributed to this report.