While the Los Angeles Dodgers are still considered the favorites to land the pitcher in a trade, the Padres remain interested in the ace.
Young major leaguers Manuel Margot, Hunter Renfroe and Austin Hedges have been discussed as possible parts going back to Cleveland.
The buzz is understandable, considering the pitcher's effectiveness on the mound over the past few years. The 32-year-old has two Cy Young awards already on his resume and came close last season before finishing in third place in the voting.
He finished the year with a 2.89 ERA and 222 strikeouts in 215 innings, plus a career-high 20 wins.
Kluber can be a game-changer at the front of any rotation if the Indians decide to pull the trigger on a deal.
Meanwhile, the Padres struggled to a 66-96 record last season but have been aggressively looking for a frontline starter throughout the winter.
In every case, the Padres have noted that top prospect Fernando Tatis Jr. isn't available, but they have a deep farm system and several quality young players that could generate interest in a deal.