A Foreign Office spokesman said, "We are aware of reports of the death of a British national in France and we stand ready to provide consular assistance".
The Chamonix mountain rescue force said the British skier could have fallen up to 1,000 metres down the north face of the Aiguille du Midi mountain.
Captain Patrice Ribes said the man and his fellow skier - who he met on the internet to arrange the excursion - would have faced driving winds of up to 100km per hour and heavy snow as they clambered back up the mountain last night.
– Captain Patrice Ribes of the Chamonix mountain rescue force
They set off earlier in the day together but then the weather turned bad.
There was a storm and so they decided to turn around and walk back to the cable car.
They left their skies on the mountain and started to climb. The British man fell from the north face at around 9pm.
He would have been exhausted from the climb. The winds were very high and the visibility, poor.
We do not know exactly how he fell. We have not found his body.
A British skier died while tackling a famous off-piste glacier in the French Alps, local police said.
The man was out with another skier when they were caught in a bad storm as they descended the challenging Vallee Blanche near Chamonix.
The British man, who has yet to be identified, plunged down the north face of the Aiguille du Midi mountain after the pair decided to return to the cable car because of dangerously high winds and blizzards.
He plummeted to his death at around 9pm following a long climb back up towards the ski lift.
Mountain rescue teams have yet to recover the skier's body.