Kershaw is under contract for $11 million in 2013. The southpaw is eligible for arbitration in 2014, then is scheduled for free agency following the 2014 season.
The two sides have discussed a number of deals, including a 10-year, $250 million deal and a 12-year, $300 million, according to Rosenthal.
If Kershaw signs for a deal worth more than $180 million, he will have signed the richest deal ever given to a starting pitcher. Felix Hernandez and Justin Verlander both signed long-term extensions this offseason; Hernandez signed a 7-year, $175 million deal, while Verlander inked a deal that will pay him $180 million over the next seven seasons.
The Dodgers have reached a tentative agreement with Major League Baseball about their deal with Time Warner Cable, and will likely want to complete the deal before signing Kershaw to an extension.