Theresa May is to visit Jordan "very, very soon" to try to strike a deal over the deportation of radical cleric Abu Qatada.
Home Office Minister James Brokenshire, who visited the state last month for talks about the case, said his boss was poised to take up the mantle.
Reports in The Sun suggest the Home Secretary has already flown out for the crunch meeting. Home Office officials said the claims were "speculation".
Mr Brokenshire told the Murnaghan programme on Sky News: "I think the discussion with the Jordanians were actually very, very useful. There was a strong recognition from the Jordanian government as to the responsibility they have for one of their own citizens.
"Yes, of course there are detailed legal issues that I discussed when I was in Jordan that are being worked through with our officials and lawyers, and the Home Secretary will be going out to Jordan very, very soon."
Qatada was released from jail under strict bail conditions while the Government seeks assurances that evidence gained through torture would not be used in any trial against him if he were sent back.
But the 51-year-old cleric, once described by a judge as Osama bin Laden's right-hand man in Europe, could be freed from his bail terms in just three months if Mrs May fails to show significant progress is being made in the talks.
Mr Brokenshire said while the Government had been "very disappointed" with the European court ruling it had upheld the principle of deporting Qatada.
"It's just working through some of the legal detail, which is why we judge it is important to get this right so when we go back to the special immigration court we can present the strongest possible case to see Qatada removed rapidly."