Home Office minister James Brokenshire will fly out to Jordan as part of the government's efforts to deport radical cleric Abu Qatada.
Number 10 officials said Brokenshire would leave on his state visit next week.
It follows Theresa May telling MPs on Tuesday that "the right place for a foreign terrorist is a foreign prison cell."
The European Court of Human Rights rejected the UK's attempts to deport Qatada to Jordan because it believed there was a risk any trial in Jordan of Qatada for terrorism offences would rely on evidence obtained by torture.
But the Home Secretary said the decision flew in the face of reassurances by Britain and Jordan that Qatada's trial would not be based on evidence gathered using torture.
Following the decision by the European Court to block Qatada's deportation, a judge in London ruled that he should be released on bail next week. The terms of the bail are house arrest 22 hours a day, no access to the internet and strict rules on visitors. He will however be able to go out for two hours each day and take his son to school.
David Cameron will also speak to the King of Jordan on Wednesday. During PMQs he told MPs "this guy should have been deported years ago. Nevertheless, if we can get that agreement with Jordan, he can be on his way."