CHICAGO -- Anything can and might happen in this strange 2020 Major League Baseball season. But could that include the Cleveland Indians and Chicago White Sox agreeing upon a trade for one of the Indians’ top starters in Mike Clevinger?

Talk of these two teams discussing a deal for the right-hander began Sunday, one day before Monday’s Trade Deadline at 3 p.m. CT, in reports from Bob Nightengale of USA Today and Ken Rosenthal of The Athletic. The Indians started Sunday one game ahead of the White Sox in the American League Central and would potentially be dealing a Nos. 1-3-type starter to a team currently featuring Lucas Giolito, Dallas Keuchel and Dylan Cease at the front of their rotation.

• Latest rumors

The White Sox have one of the best offenses in the game and could position themselves as a championship contender in 2020, let alone a contender for the division title, if they are able to add a strong arm. But general manager Rick Hahn has stated this rebuild is about sustained success over a number of years, as opposed to simply jumping up in ‘20. So, the team would not trade any of their top young players without getting contractual control in return.

In Clevinger, the White Sox maintain contractual control through 2022 or two years after this one. Clevinger was optioned to the Tribe’s alternate training site for 11 days after he and teammate Zach Plesac were caught violating team protocols by staying out past curfew in Chicago on Aug. 8.

Although Plesac was immediately sent home via car service before interacting with his teammates, Clevinger reported to the ballpark the next day and flew home with the team without disclosing he was out with Plesac. It wasn’t until Aug. 10 that it was revealed Clevinger also broke the team’s guidelines and was placed on the restricted list for four days before getting optioned.

Clevinger, who has a 1-1 record with a 3.18 ERA, last pitched on Aug. 26 at home against the Twins. After struggling to trust his surgically repaired left knee (partial meniscus tear in Spring Training) through his first three starts, Clevinger said he finally felt like he has the past few years in his last trip to the mound, where he allowed two runs over six innings while fanning six.

Cleveland would be looking for controllable pitching and an outfield bat that could provide an immediate spark to its struggling offense, as the Tribe’s group of outfielders entered Sunday collectively hitting a mere .185. It wouldn’t hurt if that bat could also provide some power, which the White Sox really don’t have to move -- unless the Indians took a chance on Micker Adolfo.

Nightengale’s report mentioned Adam Engel as part of the possible return, and while Engel has become a solid fourth outfielder and is a Gold Glove-caliber defensive player, he would not fit that power mold. Nightengale also mentioned right-handed pitcher Michael Kopech, who is the White Sox No. 3 prospect, per MLB Pipeline, as a possibility in the talked about deal.

Kopech, 24, elected not to participate in the 2020 season but is a strong part of the rotation moving forward and would seem a very unlikely piece for the White Sox to move. Dane Dunning, who made his second Major League start Sunday and threw five hitless innings against the Royals, could be in that trade mix although might hold the same value to the White Sox.