Altnagelvin Hospital has been treating large numbers of patients with Covid-19 who require high levels of oxygen.
The Western Health Trust is using 800-900 litres of oxygen per minute, around three times the normal level of usage.
Sean Gibson, head of estate management at the trust, said they have never seen this level of oxygen usage.
“I am concerned that there isn’t enough oxygen to treat patients, it’s the biggest concern,” he told the BBC.
“If we’re experiencing the growth in numbers that we have then we may not have enough oxygen to treat them. We may have to ration oxygen, it’s that serious.”
The hospital in Derry uses a green, amber and red alert system to monitor the oxygen levels.
While the levels are between green and amber, last week they were edging towards red.
Mr Gibson added: “If things continue as they are then we will be in the red very, very quickly, which is a very, very serious situation.
“This plant has never seen this type of oxygen usage.
“It’s designed to deliver but we don’t really know until we see it happening.
“I don’t think we’re going to run out of oxygen, what’s going to happen is we won’t have enough oxygen for all the patients that come through the hospital and doctors will have to think about who will get oxygen, what levels of oxygen they will be able to give them.”
However, chief nursing officer Charlotte McArdle said oxygen levels across hospitals in Northern Ireland are monitored on a daily basis with mitigation measures planned if required.
“That is one of the reasons why the Belfast City Hospital remains the Nightingale Hospital, because there is increased infrastructure and a lot of work done to ensure that it would have significant oxygen supplies to maintain a very high level of ICU,” she said.
“This is critical, oxygen is part of our medicine therapy, it is looked at on a daily basis.
“There is a situation report provided every day on this and I can assure that there is an oxygen supply available.
“I absolutely accept it is under huge demand with a high number of respiratory patients requiring assistance with ventilation and non-ventilation techniques.
“Everyone is getting the oxygen that they need and should it continue at a very high level there are other mitigations that can be put in place to make sure that everybody receives the oxygen they need, by either daily supply of cylinders or by managing the hospital network in a way that allows patients that need that high level of oxygen to be treated elsewhere.”
Meanwhile, the youngest person to die in Northern Ireland after testing positive for Covid-19 has been named locally as Aaron Doherty from Derry.
The 17-year-old, who is understood to have had underlying health conditions, battled the virus in recent weeks.
He died on Tuesday.