The decision comes after decades of protests from Indigenous groups and fans who have criticized the name as being racist. An official announcement on the decision could come as early as next week.
It was not immediately clear, according to The Times' reporting, what Cleveland intends its new name to be. One option reportedly being considered is moving forward without a replacement name initially, and consulting with the public in creating a new one.
A similar approach was undertaken in the NFL earlier this year by the Washington Football Team, which decided to stop using a name that had long been considered a racial slur.
When Cleveland will complete its transition to a new name is also unclear. A plan reportedly under consideration is to stick with the current name and uniforms for the 2021 season, and then work to shift away from the look as early as 2022.
Changing the team's name follows Cleveland's decision in 2018 to phase out the logos and imagery of its former cartoon mascot, Chief Wahoo, which had also been criticized as racist. That decision was applauded as long overdue at the time, but many insisted more had to be done.
This past July, hours after Washington announced it would be changing its NFL team's name, Cleveland's baseball franchise said it would conduct a "thorough review" of its nickname in consultation with Indigenous groups, both in Ohio and across the United States.
"We are committed to making a positive impact in our community and embrace our responsibility to advance social justice and equality," the team said in its July statement. "Our organization fully recognizes our team name is among the most visible ways in which we connect with the community."