Ms Marinova's body was found in a park in the northern city of Ruse, near the River Danube, on Saturday.
The 30-year-old reporter had most recently hosted investigative journalists on her television show who had reported on the misuse of European Union funds by Bulgarian authorities. Both were killed due to their probes into corrupt officials.
Police are investigating the rape and slaying of Marinova, 30, who was strangled.
She had recently reported on an investigation into alleged corruption involving European Union funds and made her last appearance on TV on 30 September - the debut episode of a relaunched current affairs programme called Detector.
An interior ministry spokeswoman declined to confirm or deny the information and said the ministry might issue a statement later on Tuesday.
However, Bulgarian Prime Minister Boyko Borisov lashed out at worldwide bodies and rights groups which had been quick to assume a political motive behind the murder.
While the reporter did not appear to have been intimately involved in uncovering the alleged fraud, her show touched on a sensitive subject in Bulgaria, where corruption is endemic.
Journalists' groups and foreign officials, including Harlem Desir, the media freedom representative of the Organisation for Security and Co-operation in Europe, have demanded a "full and thorough investigation" into Ms Marinova's death.
"We have collected a lot of evidence which for the time being suggests that the person is guilty".
The German government also sharply condemned the slaying, with the Foreign Ministry saying it was imperative "that there's a fast investigation and that this awful event will be illuminated as comprehensively as possible".
Speaking at a briefing attended by the chief prosecutor and prime minister, Interior Minister Mladen Marinov said on October 10 that the man was detained late the previous day at the request of Bulgarian authorities.
Ms Marinova was a director of TVN, a small TV station, and a TV presenter for two investigative programmes.
Her final show on September 30 was a program about Attila Biro, an investigative journalist with the Rise Project Romania, and Dimitar Stoyanov from the Bulgarian investigative site Bivol.bg.
"We have detained a man".
The minister said investigators had spoken to Marinova's family and friends and "there is no apparent link to her work".
After her death, prosecutors opened an investigation into GP Group, the private Bulgarian building company that Biro and Stoyanov spotlighted in their report, according to The Associated Press.