The aluminium smelter uses energy from the nearby nuclear power station
Anglesey Aluminium Metal (AAM) aims to "safeguard operations" at the site, says parent firm Rio Tinto, which is cutting 14,000 job worldwide.
Mining firm Rio Tinto, which has a 51% stake in the smelter, is closing one of its London offices as part of cuts in its 97,000-strong global workforce.
Anglesey Aluminium employs 515 staff and 50 contractors on the island.
Rio Tinto said AAM was still looking for an alternative energy source from October next year.
Anglesey Aluminium Metal is a joint venture between Rio Tinto and its partner Kaiser Aluminium (which has a 49% stake in the Welsh plant).
In the past few months, Rio Tinto, the world's third-largest mining firm, has been fending off a takeover approach from rival BHP Billiton, which finally abandoned its offer in November.
It has announced plans to reduce its debt by $10bn (£6.8bn) by the end of next year.
The plans include combining its two London offices. Less than 2% of Rio Tinto's workforce are based in the UK.
Anglesey Aluminium runs its smelting operation on a 250-acre site using electricity produced by the Wylfa nuclear power station situated nearby.
Wylfa is due to close in 2010 and as yet there has been no decision on whether a Wylfa B or an alternative source of electricity will be built.
In a statement Rio Tinto s job cuts plans, Anglesey Aluminium said it was working "at assessing viable scenarios to safeguard operations on site beyond October 2009" but this required "a competitive and reliable source of energy" to be in place.
The firm said: "AAM continues to investigate all options to secure affordable power for the period commencing October 1st, 2009, including a deal with the Nuclear Decommissioning Agency (NDA).
"AAM is also exploring avenues with partners and stakeholders to further develop other long-term options in line with existing operations, the needs of the local community and the economic market situation.
"AAM will work at minimising the impact to its employees and contractors."
Councillor Phil Fowlie, Anglesey council Leader said: "The county council remains in regular direct contact with Anglesey Aluminium.
"Today's announcement by Rio Tinto is obviously cause for concern.
"The Holyhead smelter is one of the island's main employers, providing quality jobs to its 550 work force as well as many external contractors.
"We now await to find out if Rio Tinto's announcement will have a direct impact on the plant here in Anglesey."