The birds are nesting on a chimney at Thrigby Hall Wildlife Gardens near Great Yarmouth and are involved in mating rituals, experts say.
The white stork breeds in continental Europe, migrating to Africa in winter.
The last record of storks breeding in Britain was at St Giles' Cathedral, Edinburgh, in 1416.
Source: RSPB
Ken Sims, director of the wildlife gardens said: "We gave the storks a helping hand by building a structure for their nest on the hall's front chimney.
"But they turned their back on our handiwork and have built their own nest on one of the rear stacks."
He said he thought the female stork was on the point of laying and they had been watching them mate.
"The beaks are used like clappers and they throw their heads back," he said.
"They greet each other with lots of clicking and clacking."
The nesting birds are part of the collection at the wildlife gardens and director Ken Sims said they had been trying to get storks to nest for many years.
"We've kept them for a number of years but they have been pinion birds [flight feathers on one wing have been removed} and have occasionally bred on the ground.
"But to have them free-flying and nesting as they would do in the wild is very rare."
A pair of white storks nesting in Norfolk could be the first in the UK to breed from a traditional nest for nearly 600 years.