Hitachi, the company behind the Wylfa Newydd project on Anglesey, said "no formal decision" has been made on the future of the site.
Addressing reports it was planning on suspending the project on Anglesey, it said it is not "based on Hitachi's decision" but it "has been assessing the Horizon project including its potential suspension and related financial impacts".
A report in 2015 said the multi-billion pound investment was a "once in a generation" opportunity for Welsh businesses.
Almost 7,000 people are expected to be involved in the construction of the plant.
GMB, the union, is calling on the UK government to step in to ensure the construction of the £20bn power plant and says it would leave the UK's energy plans "reduced to tatters" if it does not go ahead.
The UK Government entered into negotiations with Hitachi in June to consider investing in the project.
First Minister Mark Drakeford tweeted to say the reports are "worrying".
The group PAWB (People Against Wylfa B) said should the news be confirmed, then it will be "a relief" for those who "worry about the future of our Island, our country, our language, our environment and indeed renewable energy."
Dr Doug Parr from Greenpeace UK said it is "the chance to think again and make a better decision."