"We are looking into the [Ratanang family] trust, and whatever any avenues our investigation brings us to,"Hawks spokesman McIntosh Polela said.
"We will not be taking cues from the media in our investigation. We have our own ways of finding stuff out."
He said the Hawks made the decision to initiate the investigation over a week ago.
"There is a lot that we have to go through, so it is difficult for us to say when the investigation would be completed. We are not committing to a specific date yet."
He said the unit would take action against Malema based on the results of the investigation.
This follows the African National Congress' announcement on Friday of dates for disciplinary hearings for both Malema and party spokesman Floyd Shivambu.
Malema recently said the league would send a team to Botswana to consolidate local opposition parties and help bring about regime change. It believed the government there was "in full co-operation with imperialists" and undermining the "African agenda".
The ANC publicly rebuked the league. The league in turn said it did not believe it was in the wrong or going against ANC policy. It expressed disappointment at being publicly rebuked before the matter had been internally discussed.
The hearings would take place on August 30 and 31.