The former head of the CIA and the NSA, General Michael Hayden, dampened speculation on Monday that the US might offer a plea bargain to Edward Snowden, the NSA whistleblower.

Hayden, speaking at an Oxford University lecture, said that while deals had been done with other leakers in the past, he detected little enthusiasm for such a deal for Snowden.

His comments come after the US attorney-general Eric Holder and others within the Obama administration hinted at a possible plea bargain.

Snowden has temporary asylum in Russia until July and in the event of being refused an extension would have a further year in the country to appeal. In spite of sympathy for him in many western European countries, none of their governments are prepared to risk angering the US by granting him asylum.

Hayden used a 90-minute lecture and question-and-answer session at Pembroke College to defend the NSA and Britain's GCHQ from the controversy created by the leak of the Snowden documents.

In a surprise admission, Hayden portrayed the reforms recently announced by Barack Obama in the wake of the controversy as limited, with the president allowing the intelligence community "a pretty big box" in which to continue to operate.

Some of the changes were more than just cosmetic, he said, but overall the president and the intelligence community could largely continue as before.

Asked by the Guardian about a deal that would see Snowden return to the US without a hefty prison sentence in exchange for a return of the tens of thousands of leaked documents, Hayden referred to deals done in the past.

"There have been arrangements but I do not think there is a lot of enthusiasm inside the US for that kind of deal [in the case of Snowden]," Hayden said.

Referring to what he described as the "excitement" of the last eight months since the first batch of Snowden stories appeared, Hayden said that heads of the NSA and GCHQ must be looking every morning with apprehension at the next story. There was a rhythm of a new accusation every seven to ten days that had left the governments in the US and UK on the back foot, he said.

Hayden accused the Guardian the Washington Post and Der Spiegel of hyping the issues. But he acknowledged they had provided a service too. "I freely admit that what these writers and writers like them have done has accelerated a necessary and frankly inevitable discussion," he said, while adding they had "misshaped the discussion".

The main failing of the media had been its failure to provide context, he said – like arriving towards the end of a film and trying to work out who was the good guy and the bad guy.

That context missed by the media, Hayden said, included the post-cold war change from challenges posed by a state to those posed by stateless terrorists ; the technological revolution that brought about the internet; and cultural differences about privacy in the US and Europe.

Damage had been done to the NSA, with terrorists changing their methods of communications, he claimed.

On the recent announcement by Obama in response to the controversy, he said the president had essentially backed the NSA.

Some of the reforms, Hayden felt, were more than cosmetic and would be burdensome for the NSA, but he said on the whole that the agency still had a lot of room for manoeuvre, and would continue to collect metadata.

Although President Obama had said he would order an end to listening into the calls of friendly leaders, Hayden noted that this would only apply until such time as the US decided there was a good reason to hack the calls.

"I guess what I am saying is this president, who most people view as being quite different than his predecessor, doubled down on a programme being done under his predecessor. He gave the American intelligence community a pretty big box," Hayden said.

"The president is essentially trading some restraint, some oversight, in order to keep on doing fundamentally what he has been doing."