Kershaw is joined by Pittsburgh outfielder Andrew McCutchen — the 2013 winner — and Miami outfielder Giancarlo Stanton as the NL MVP finalists, the Baseball Writers' Association of America announced Tuesday.
Cincinnati's Johnny Cueto and St. Louis' Adam Wainwright are competing with the Los Angeles left-hander for the NL Cy Young.
Since Gibson won both awards in 1968 along with Detroit's Denny McLain, six AL pitchers have swept MVP and Cy Young in the same year: Oakland's Vida Blue (1971), Milwaukee's Rollie Fingers (1981), Detroit's Willie Hernandez (1984), Boston's Roger Clemens (1986), Oakland's Dennis Eckersley (1992) and Detroit's Justin Verlander (2011).
In the AL, the MVP finalists are Cleveland outfielder Michael Brantley, Detroit designated hitter Victor Martinez and Los Angeles Angels outfielder Mike Trout, who finished second to the Tigers' Miguel Cabrera in each of the last two votes.
The Cy Young finalists are Chicago White Sox left-hander Chris Sale, Seattle's Felix Hernandez and Cleveland's Corey Kluber.
Mets pitcher Jacob deGrom, Cincinnati outfielder Billy Hamilton and St. Louis second baseman Kolten Wong are competing for NL Rookie of the Year. Chicago White Sox first baseman Jose Abreu, New York Yankees reliever Dellin Betances and Angels right-hander Matt Shoemaker are the AL finalists.
San Francisco's Bruce Bochy, Pittsburgh's Clint Hurdle and Washington's Matt Williams are the NL Manager of the Year finalists, and Baltimore's Buck Showalter, the Angels' Mike Scioscia and Kansas City's Ned Yost are vying for the AL honour.
Three of four managers of wild-card teams are among the finalists; Hurdle won the NL balloting last year.
Voting took place before the post-season, when the Giants beat the Royals in a seven-game World Series. Winners will be announced next week live on the MLB Network, beginning Monday with the rookies of the year and concluding Thursday with the MVPs.