A person with knowledge of the talks also told MLB.com that they do not believe the Padres have passed the Dodgers as the favorites to land the two-time Cy Young Award winner.
Kluber, 32, posted a 2.89 ERA and a 20-7 record in 33 starts last season for the Indians. The three-time All-Star also led Major League Baseball with two complete games and one shutout. He led the American League with 215 innings pitched.
The right-handed ace led baseball with 18 wins, a 2.25 ERA, five complete games and three shutouts during his Cy Young Award winning 2017 campaign with the Tribe. Kluber is 96-55 with a 3.09 ERA in eight seasons with the Indians during his baseball tenure.
He is due $17 million in 2019 and has a $17.5 million team option in 2020 with a $1 million buyout. He has an $18 million team option in 2021 with another $1 million buyout.
Kluber was initially a fourth round pick by the Padres in the 2007 MLB Draft, but was traded to the Indians in 2010 as part of a three-team trade involving the St. Louis Cardinals.