Acta, fired by the Nationals in July, will meet with Indians owner Paul Dolan, general manager Mark Shapiro and other front-office personnel on Tuesday at Progressive Field. The Indians said Acta will be available to the media afterward.
"It's the type of meeting in which you have to be at the park from 8 in the morning until 5 in the afternoon," Acta told ESPNdeportes.com's Enrique Rojas. "Teams want to know the opinion of a potential manager in regards to all areas of the team."
ESPN analyst Bobby Valentine, whose New York Mets reached the World Series in 2000, is also a finalist for the job and will undergo a second interview in Cleveland this week, The Plain Dealer has reported.
The Indians are bringing as many as five finalists to Cleveland for second interviews after phone interviews last week.
Acta, 40, went 158-252 in two-plus seasons for the Nationals. He was fired after the team started 21-61 last season.
Acta interviewed for Houston's managerial job last week.
"I feel truly optimistic about the opportunities to go back to the MLB [in a managerial role]," Acta told Rojas. "My initial talks with both organizations were satisfactory."
Acta has a long connection to the Astros, who drafted him as a 17-year-old. He played six seasons in their organization and later managed Houston minor league affiliates for eight seasons.
Before managing in Washington, Acta coached in Montreal and for the Mets.
The Indians fired Eric Wedge in September, a few days before they finished 65-97 and tied Kansas City for last place in the AL Central.
Acta has experience dealing with young players and has been through a rebuilding project before, two attributes that could make him appealing to the Indians. Cleveland is considered to have more talent than Washington and could bounce back next season because it plays in one of baseball's weaker divisions.
Information from ESPNdeportes.com's Enrique Rojas and The Associated Press was used in this report.