Baseball writer Robert Murray reported the news Thursday and noted the Tribe's asking price is "crazy high."
Clevinger has quietly emerged as one of the top starters in the American League over the last three years. The 2019 season was his best to date as he posted a 2.71 ERA and 1.06 WHIP with 169 strikeouts in 126 innings across 21 starts.
His 10.7 WAR since the start of the 2017 campaign ranks 17th among all MLB starting pitcher, one spot behind Dodgers ace Clayton Kershaw (11.0), per FanGraphs.
In all, the 28-year-old (he'll turn 29 on Saturday) Florida native has compiled a 3.20 ERA and 1.19 WHIP in 97 appearances (84 starts) across four seasons with Cleveland.
"He's really tough," Minnesota Twins manager Rocco Baldelli told reporters about Clevinger in September. "He misses about as many bats as anybody in baseball. His stuff is excellent. He executes pretty well. It's never an easy day when you're facing him. You know you're going to have to pull some things out to make it happen."
Clevinger's trade value is bolstered by the fact he's under team control via arbitration through 2022, including an estimated $4.5 million salary for 2020, according to Spotrac.
Although it's unlikely the Indians would be motivated to move him given his performance in recent years and that contract situation, it's possible a bidding war between NL West rivals L.A. and San Diego would at least create an offer worth considering for the Cleveland front office.
Clevinger would give the Dodgers one of the most promising rotations in all of baseball, especially a top three of Kershaw, Walker Buehler and the current Tribe star.
He'd take on a more prominent role within the Padres' starting staff, where he'd likely serve as the ace ahead of Chris Paddack and Joey Lucchesi.