Salvors and naval architects are monitoring the wreck to ensure it remains safe to work on and divers are being used to survey the area around the submerged rear section of the ship.
Attempts are also being made to source a remote operated vehicle to help with mapping while large numbers of damaged containers and debris remain on the sea floor around the wreck.
Overcast weather and choppy seas around Rena are expected to continue until tomorrow.
Next week, container recovery company Braemar Howells will focus on further cleaning of Matakana's beaches, including lifting piles of stacked wood and timber on to a barge offshore.
Spokesman Grant Dyson said the wooden structure, resembling a giant Jenga game, built by the public from timber washed up at Orokawa Bay, just north of Waihi Beach, had been removed for safety reasons.
Maritime NZ spokesman Ross Henderson said small amounts of oil continued to trickle from Rena, producing a light sheen on the water. Thirty people were working on the clean-up at Matakana Island yesterday and two teams of 15 each were working at Mount Maunganui and Leisure Island.
A team of five was also working at Ongare Point, north of Katikati.
Weather permitting there are tentative plans to release eight little blue penguins back to the sea next week.
Seventeen penguins and a grey-faced petrel are being cared for at Massey University, with another four being cared for in Tauranga.
The wildlife rescue centre at Te Maunga has been largely dismantled and will soon be passed back to its owners, Tauranga City Council.
