ESPN Deportes first reported Acta interviewed for the job.
Dan Jennings is expected to remain as manager through the rest of the season. After that, it is unclear if he will return to the front office. Jennings transitioned from general manager to manager, replacing Mike Redmond on May 18.
Jennings, who is signed through 2018, may seek opportunities with other organizations. He's already been linked to front office positions with the Phillies, Orioles and Mariners.
Jennings took over a 16-22 squad, and the Marlins entered Tuesday night against the Phillies at 64-86. If Jennings is not back as general manager, Jeff McAvoy, Miami's director of pro scouting, is an internal choice to be promoted to general manager.
Michael Hill is expected to remain as president of baseball operations.
The Marlins also are expected to retain much of their core players, and build around All-Stars Giancarlo Stanton and Jose Fernandez.
A number of candidates are expected to emerge. Although Dusty Baker fits the mold, and was linked to the Marlins when Redmond was replaced, a source told MLB.com that Baker is not a candidate at this point.
Some other possibilities include Jim Riggleman, Bud Black and Larry Bowa.
The Marlins are winding down a disappointing 2015, which has been plagued by injuries and underperformances.
When Jennings took over as manager, he didn't have any previous coaching or managing experience at the professional level.
Acta, 46, has a combined 372-518 record combined managing the Nationals and Indians.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.