The directive came following reports that the UK has issued an alert to airlines around the world urging them not to allow the former CIA employee to board flights to Britain.
The British government told carriers to deny Snowden passage on UK-bound flights because "the individual is highly likely to be refused entry to the UK", the Associated Press said.
The news agency reported that it had seen a photograph of an "alert" with a Home Office letterhead taken today at a Thai airport issuing the directive.
The United States launched a criminal investigation after Snowden, a former CIA technical assistant, blew the lid on the National Security Agency's vast electronic surveillance operation.
More From This Section
Today, US Attorney General Eric Holder said he was confident Snowden would be prosecuted for "extremely damaging" leaks.
The 29-year-old, who remains in hiding in Hong Kong, has vowed to fight any bid to extradite him.
A Malaysia Airlines spokeswoman in Kuala Lumpur told AFP today the carrier had received a notice asking it not to allow Snowden to board flights to the UK.
The notice was marked as a "message from UK border" said the spokeswoman.
"Apparently the notice came from UK Border. So don't allow him on flights to UK," she added.
In Hong Kong a Cathay Pacific Airlines spokesperson told AFP it would "not discuss communications, if any, received from governmental agencies" due to security reasons.
The city's airport authority said it had not received any instructions about banning Snowden from boarding flights.
Virgin Atlantic's press office in Britain said it would not comment on issues of "national security".