Meanwhile, commissioner Rob Manfred has warned the players union that the season could be shut down as soon as Friday if players don't do a better job following league protocols - from the more egregious things like going out to bars, to on-the-field no-nos like high-fives and spitting.
The Miami Marlins have also had their season suspended through at least Sunday, with 18 players reportedly having tested positive, in addition to two staff members.
Should another outbreak materialize, Manfred has the power to shut the season down.
Díaz consistently tested negative while the season was on hold, but he made a decision to become the first Miami player to opt out.
Manfred and Clark talked about what needs to be done to finish the season, a person familiar with the conversation said.
Most recently, the game between the Brewers and Cardinals was postponed after St. Louis had two positive tests, according to Jon Heyman of MLB Network. On Thursday afternoon came news that the Philadelphia Phillies are suspending all activities at Citizens Bank Park after two positive tests in that organization, identified only as a coach and a clubhouse staffer.
Both outbreaks occurred during road trips, with the Cardinals' believed to have originated in Minneapolis, where they played against the Minnesota Twins before continuing on to Milwaukee. "Players are seeing what can happen", Houston manager Dusty Baker said. The Cardinals had played at Target Field on Wednesday, a day before the Indians arrived.