"They are doing seismic surveying to ascertain the nature of the substrata of the sea floor," said Mr Joyce.
If a well was created, it would cost up to $100 million and was at least five years away.
The Government could take up to 45 per cent of the profit in royalties and taxes if the well was successful.
Anadarko has been criticised for its stake in the Gulf of Mexico oil spill. It had a 25 per cent share in the Deep-Water Horizon rig which exploded in 2010, killing 11 workers and spilling an estimated 190 million gallons of oil into the Gulf. Anadarko has denied liability in the incident.
In June, a representative of Anadarko said that a deep sea oil blowout in NZ could take up to two weeks to be capped.
Mr Joyce also emphasised more information communication technology (ICT) businesses could be developed here.
This was supported by the Government through the Rural Broadband Initiative.
"This is key to ensuring Wairarapa remains strongly connected."
He cited Masterton businesses Harvest Electronics and CRS Software as good examples of local ICT businesses.
Jobs in the area were reliant on the country's economic success, he said.
"Overall the economic climate is really important, it's about NZ doing well."
If housing demand improves, it would be good for Juken Mill, for example, he said.
"If dairy grows then the development of Pahiatua makes more sense."
For people struggling to find work, this would create flow-on effects like jobs, said Mr Joyce.
He also said local education providers like UCOL and Taratahi provided good training opportunities.
"It's good [for Wairarapa] to have a specialist agricultural training provider."
"There is a shortage of people in forestry and agriculture."
Mr Joyce is also Minister for Tertiary Education, Skills and Employment and said student loan living costs and student allowances were enough to live on.
The maximum student loan for living costs is $172.51 a week.
Average rent for Masterton in a flat of three was $120, according to TradeMe, which would leave a student just over $50 for food and bills.
"It has been historically enough to live on," said Mr Joyce. "It's no better or no worse."
He said the Government had raised the living costs with inflation and compared to other countries, the minimum wage was quite high.
In fact, the number of full-time students was growing, he said
Next year, fees-free foundation courses would be on offer at polytechs and private training organisations, Mr Joyce said.
The recent US Government shutdown may have some impact on NZ, said Mr Joyce.
"It could do if it went on long enough.
In the short term, however, he was not overly concerned.
"It wouldn't create a recession partly because of the strong demand for NZ exports."
