A Nikos representative was unavailable to comment about the 549 St Kilda Road speculation.
Fitzroys selling agent Marc Leiber, believed to be behind the off-market deal, declined to comment when contacted by Capital Gain.
The building failed to sell when it was listed for sale at the start of the economic downturn two years ago.
Sources expect Nikos will fill the office space and retain the asset as an investment, though residential redevelopment down the track is an option.
The office building replaced the historic Koonwarra mansion, and was part of a push from the 1970s to redevelop grand mansion sites in St Kilda Road, into offices, which are now amongst the cheapest in Melbourne to lease.
Nikos owns another asset in the area at 580 St Kilda Road.