Geoff MacLellan says about half the derelict ship has already been cut up and shipped away for scrap and all of the contaminated material has been removed from the edge of Scatarie Island.
He says once the last scraps from the former bulk carrier are removed, crews will then be called on to dismantle their work camp.
Still, MacLellan says the cleanup should be completed before the fishing season starts.
He says Ottawa has yet to respond to a request for financial assistance, though he said he believes federal officials are probably waiting for the final cost of the cleanup.
But the federal transport minister has already rejected the plea for money, saying last year that the cleanup isn't an impediment to navigation and therefore Transport Canada is not be involved.
MacLellan says the total cost will exceed the original $11.9-million budget because of the extra asbestos and diesel fuel found aboard the vessel, which was almost five times more than estimated in federal reports.
The company tasked with removing the ship has taken 30 tonnes of asbestos from the vessel to date, far more than the 6.6 tonnes of asbestos federal reports estimated to be on the ship.
MacLellan has said Ottawa should contribute because the wreck posed an environmental threat to Scatarie Island, a provincially protected wilderness area.
The 12,000-tonne, 223-metre bulk carrier ran aground on the island after a tow line snapped in rough seas during transit to Turkey from Montreal in September 2011.