The Forestry Commission said the plan could be introduced to stop people inadvertently spreading the infection by carrying fungus on their boots.
Earlier this year the commission closed Knockmountain forest in Scotland near Glasgow to the public after discovering infected ash trees.
Officials are now considering similar restrictions at forests in the East of England which have been infected.
The fungus, Chalara fraxinea, which has severely affected other European countries and now spread to Britain, kills 90 per cent of trees it infects.
On Monday the Government banned ash imports to Britain, but experts warned that it may be "too little, too late".
They believe that Britain faces an environmental catastrophe on the scale of the Dutch Elm disease outbreak, which killed 25 million trees in the 1970 and 80s.
More than 100,000 trees have already been destroyed in an attempt to stem the spread of the disease. Officials are now considering further moves, such as placing restrictions on movement and enhanced biosecurity.
A spokesman for the Forestry Commission said: "What we would do is require greater biosecurity. The Forestry Commission in Scotland has closed Knockmountain forest to the public.
"It [the fungus] could get on your boots and you could walk with it into other gardens. It helps prevent the spread."
Pound Farm, a 90 hectare woodland in East Anglia, has suffered one of the worst outbreaks of the fungal disease.
Thousands of ash trees are infected and the Woodland Trust, which owns the site, believes it is too late to destroy them.
Norman Stark, operations director at the Woodland Trust, said: "It is very depressing, and difficult to know what we can do. If you start felling the trees you make the spores fly further. We may already have lost this battle."
Mr Stark said the trust would be prepared to close the woodland if advised to do so by the Forestry Commission. He was sceptical, however, about whether it would be effective.
He said: "They have tried to use a policy of containment in Norway but the evidence is that it hasn't worked. The fungus is in all the leaves and keeping people out of forests and English woodlands is very difficult.
"But we would be happy to do whatever is necessary, if it was shutting the site then it wouldn't be a problem."
The outbreak was first detected in a nursery in February. It has since spread to more than 20 sites across the country.
The government has faced repeated criticism for failing to ban the import of ash plants from the continent.
Yesterday it emerged that the Forestry Commission was warned in 2009 about the threat posed by the disease. It was urged to block imports, but failed to do so.
The National Trust yesterday said it was checking ash trees on its grounds throughout the South and South East of the country for signs of the disease.
Ian Wright, the National Trust’s plant health specialist, said: “We are particularly concerned about the significant number of our older ash trees. Many, over 300 years old, grow on National Trust land. If this devastating disease took hold it would radically change some of our most special landscapes and places forever.”
