But anti-nuclear group Pawb says it has concerns about Wylfa's vulnerability to cyber-attacks and air assaults.
Wylfa is defended by the Civil Nuclear Constabulary (CNC), an armed force dedicated to counter-terrorism.
Secretary of State for Wales Cheryl Gillan welcomed the inclusion of Wylfa on the shortlist.
The future of the smelting plant, Wylfa's main customer, is tied into the power station.
Up to 6, 000 jobs could be created while the new reactors are built at Wylfa.
He said Wylfa represented an "extremely attractive investment opportunity" and there remained considerable interest in it.
The station is due to close after that date and plans for Wylfa B are on hold.
Wylfa is the only Magnox site still generating electricity, following the closure of Oldbury in Gloucestershire in February.
He added the Horizon site at Wylfa represented an "extremely attractive investment opportunity" and there remains considerable interest.
David Jones said securing a new nuclear station, Wylfa B, on Anglesey was "critical" to his economic efforts.
The site employs about 650 directly, while an estimated 500 jobs rely on Wylfa through contractors and suppliers.
First Minister Carwyn Jones said Wylfa was key to the economy of Anglesey.
Mr Jones said he was committed to working towards securing a new generation nuclear power station at Wylfa on Anglesey.
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These include building homes for construction workers who would be involved in building a new nuclear power station at Wylfa.
He often returned home to Anglesey to mother Ellen and father Ian, who works at the Wylfa Nuclear Power Station.
The island's nuclear station Wylfa is due to end production by 2014 but there are hopes of a new station.
Dylan Morgan, of People Against Wylfa B (Pawb) said the plant should be closed, as planned in December this year.
The Horizon project to build new reactors at Wylfa and Oldbury, Gloucestershire, was put up for sale by German-owned E.
National Grid is consulting over proposals to transfer power from offshore wind farms and Wylfa B to the electricity network.
Carl Iwan Clowes, of People Against Wylfa B (Pawb), said the waste from nuclear power stations created problems for future generations.
If given the go-ahead, a plant would be built nearby to replace the existing Wylfa station, due to be decommissioned in 2012.
Hitachi is buying Horizon Nuclear Power, which was intending to build reactors on existing sites at Wylfa, Anglesey, and Oldbury, near Bristol.
In the long term, said Mr Morgan, the Anglesey Aluminium company was not interested in a new nuclear power station to replace Wylfa.
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The Horizon nuclear scheme, which includes a new Wylfa plant to replace the existing Magnox one, was put up for sale in March.
The Welsh Affairs select committee published its energy report the same day it was confirmed Wylfa nuclear power plant would close in 2010.
They also argue that they could all see an increase in pupil numbers if a new nuclear power station is built at Wylfa.
The Japanese company will push ahead with plans to build two to three 1, 300 megawatt nuclear power plants at both Wylfa and Oldbury.
But this one coincides with concerns about the development of the new Wylfa B site, in the wake of the nuclear emergency in Japan.
Developer Horizon Nuclear Power has previously said it hopes to lodge a planning application for the new Wylfa plant by the end of 2011.
Stuart Law, the site director at Wylfa, said he was grateful David Jones had visited the site at a "crucial time in Wylfa's lifecycle".
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