Discussions continue between the Dodgers and Indians about a blockbuster trade that could result in a two-time Cy Young Award winner joining Clayton Kershaw in the Los Angeles rotation.

Sources say the Dodgers and Indians have discussed various trade proposals in recent days. One such possibility involves Cleveland ace Corey Kluber going to Los Angeles in a deal that includes Yasiel Puig .

The Dodgers would need to add at least one significant player in addition to Puig in order for the Indians to seriously consider moving Kluber, one source said Wednesday. MLB Network insider Ken Rosenthal was first to report the talks between the Dodgers and Indians.

In addition to Puig, the Dodgers have catching-prospect depth and would likely be willing to move left-hander Alex Wood and right-handed prospect Yadier Alvarez, who was just recently added to Los Angeles' 40-man roster.

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The availability of Kluber and fellow right-handers Carlos Carrasco and Trevor Bauer reflects realities of Cleveland's market size and current roster. A trade involving one starter would allow Indians officials to add young talent to an experienced core while freeing up payroll space to pursue necessary outfield and bullpen upgrades.

For now, sources say the Indians are maintaining high price tags on Kluber, Carrasco, and Bauer, and are not yet close to making a major trade. Including team options, Bauer and Carrasco are under club control through 2020, and Kluber through '21.

The Brewers and Braves are two more potential trade partners for the Indians if they move a starter. While the Braves and Indians are not currently in active talks, one source said, Atlanta has pitching prospects (including right-hander Kyle Wright ) that appeal to Cleveland. The Brewers possess both young pitching depth and outfielders (Corey Ray and Keon Broxton ) who fit the Indians' needs.

Kluber has finished among the top 10 in American League Cy Young Award balloting in each of the last five seasons -- including four times in the top three. He's one of only two Major League pitchers to throw 1,000 regular-season innings since 2014. Max Scherzer is the other.

Kluber, who turns 33 in April, avoided the disabled list in 2018, but he required a pain-relieving injection in his right knee at the All-Star break in order to make it through the second half. Kluber started two games on short rest in the 2016 World Series; he is winless with a 10.64 ERA in three playoff starts since then.