Shares in the Japanese company soared by 9% on the Tokyo market after the Nikkei business daily reported it was to put the plan for the £20bn Anglesey plant on hold.
Hitachi said "no formal decision" had been taken on the Wylfa Newydd project, but acknowledged its suspension was an option.
It follows concerns about rising building costs.
The halting of the scheme would represent a major blow to the North Wales economy, with the plant expected to provide 8,500 jobs at the height of its construction.
Once up and running by the mid-2020s it was set to create up to 850 permanent jobs, many of them highly skilled.
It would also serve as a setback to the UK government's drive to move away from the reliance on dirty coal and meet global climate targets.
The 2900 MW plant, which under the proposals would be built on a site next to the former Magnox Wylfa power station, could provide around 6% of Britain's energy needs
A Welsh Government spokeswoman said: "This is a major project with potentially significant economic benefits to Anglesey, North Wales and Wales.
"We will continue to monitor the situation very carefully and press the UK Government do to everything it can to help bring this project to Anglesey."
A spokeswoman for Theresa May said talks with Hitachi were continuing.
"On Hitachi, the negotiations on that are ongoing and those are obviously commercially sensitive so I can't comment," she said.
In a statement, Hitachi said: "No formal decision has been made in this regard currently, while Hitachi has been assessing the Horizon project, including its potential suspension and related financial impacts in terms of economic rationality as a private company."
A spokesman for the UK government's Department for Business, Energy and Industrial Strategy, said: "Negotiations with Hitachi on agreeing a deal that provides value for money for consumers and taxpayers on the Wylfa project are ongoing.
"They are commercially sensitive and we do not comment on speculation."
Towards the end of last year, Toshiba scrapped its UK nuclear venture behind the development of the planned Moorside power station in Cumbria.
The Japanese engineering firm revealed its NuGen project was to be shut down after its US reactor unit Westinghouse went bust.
Sue Ferns, deputy general secretary of the Prospect union, said: "This is extremely worrying news, especially coming in the wake of Toshiba's recent withdrawal from the Moorside project.
"To lose one major nuclear project is a serious blow, to lose two in six months would set alarm bells ringing about the sincerity of the government's commitment to new nuclear."
She added: "New nuclear is of significant strategic importance for the country, the government must not sleepwalk into an energy security crisis by allowing these projects to fail one by one."
Tom Greatrex, chief executive of the Nuclear Industry Association said it was "imperative" that the project went ahead.
"If the UK is going to decarbonise its power supply and meet our obligation to reduce carbon emissions, we need to replace the 20% of our electricity delivered by our low carbon, reliable, secure nuclear fleet, most of which will retire in the next decade," he said.
Dr Doug Parr, chief scientist for Greenpeace UK, said: "The government's energy policy is in tatters, but this is the opposite of a disaster.
"We could have locked ourselves into reliance on an obsolete, unaffordable technology, but we've been given the chance to think again and make a better decision.
"The failure of the old technology is the opportunity the new technologies need, and Britain's world-leading offshore wind industry's time has come."