Gauri Lankesh was shot outside her Bengaluru home on the evening of September 5.
The man who shot her had been wearing a motorcycle helmet.
He had arrived at the scene on a motorcycle with another man.
"If there is no proper evidence when we file the charge sheet in the court, it won't stand. So we are trying to collect the evidence properly. We know who has done it (the killing) and what.... everything we know," PTI quoted Reddy as saying.
"We have got clues, but we cannot tell things to the media for now because we should have correct evidence for the clues we have got," Reddy said.
PTI added that Reddy had on September 9 made similar claims of having found "some clues" related to the murder of Gauri Lankesh.
Lankesh's murder had incited huge outrage and protests around the country.
Lankesh edited the anti-establishment Gauri Lankesh Patrike.
The general consensus is that she was murdered for her views.
Lankesh's killing was very similar to the earlier killings of the rationalists and activists Govind Pansare, Narendra Dabholkar, and MM Kalburgi.
Like Lankesh, they were killed by motorcycle-borne men. And like her, they were severely critical of the right wing.