Indians close to giving Corey Kluber new multiyear deal

— -- The Cleveland Indians are on the verge of a multiyear contract extension with 2014 American League Cy Young Award winner Corey Kluber, a baseball source told ESPN.com on Saturday.

Kluber, 28, enjoyed a major breakthrough in 2014, posting an 18-9 record with a 2.44 ERA and 269 strikeouts. He overtook Seattle's Felix Hernandez in the Cy Young race down the stretch and joined Gaylord Perry,  CC Sabathia and Cliff Lee as the fourth Indians pitcher to win the award.

A source confirmed the Indians have also had discussions with pitcher  Carlos Carrasco on a mulityear extension. But it's not clear whether the two sides are close to an agreement.

Carrasco, a five-year veteran, is coming off a year in which he logged career bests with 134 innings, 140 strikeouts and a 2.55 ERA.

Kluber broke into professional ball as a fourth-round draft pick with San Diego in 2007. The Indians acquired him in July 2010 in a three-way trade with the  Padres and St. Louis Cardinals.

Kluber, who has only two years of major-league service time, agreed to a $601,000 contract with the Indians in mid-March. He was the last player on Cleveland's 40-man roster to agree to terms.

The Cleveland Plain Dealer reported progress in Kluber's talks with the Indians earlier Saturday, and Foxsports.com was first to report that Kluber was close to an agreement with the club.