The coalition is confident it will find the al-Qaeda leader
He told the BBC that he was confident that the US-led forces would find the terror leader or he would be given up soon.
And he said that British troops were ready to travel to Afghanistan "at very short notice."
No decision has been taken on their deployment but Downing Street has indicated that there have been "detailed discussions" with the United States over the use of UK forces in "overt" operations.
Results promised
Mr Hoon told BBC Radio 4's Today programme that the pressure on the Taleban regime and Bin Laden from air strikes and advances by the Northern Alliance would have results.
He admitted the anti-terrorist coalition still did not know where Bin Laden was living but said that they were a lot closer to finding the al-Qaeda leader than two weeks ago.
"The areas in which he can freely move are now distinctly limited," he said.
"I am confident that in due course, either we will find him or someone else will give him up."
He said that the government had always said that sending British ground troops was an option.
"No specific decisions have yet been taken but clearly we are exploring all of the possibilities," he said.
"We always have troops ready to go at very short notice."
Questioned whether Bin Laden would be specifically targeted by military action, the prime minister's official spokesman said: "It's not a video game, there are bound to be casualties - war is not a clean business."
Ground offensive
Britain has always said it would respond positively to US requests for assistance, which so far has included launching cruise missiles from nuclear submarines and help in refuelling and reconnaissance work.
The spokesman said Prime Minister Tony Blair would be "completely straight" with the British public on what casualties to expect if and when troops go into action on the ground.
But he declined to comment on speculation that SAS special forces were already on the ground in Afghanistan, where the US deployed troops on Friday.
BBC defence correspondent Paul Adams said British troops which could be used in a ground offensive included the SAS, Royal Marines Commandos and Pathfinder Platoon from 16 Air Assault Brigade.
UK Foreign Secretary Jack Straw, in a speech on Monday, said he could not speculate about the timing of a possible deployment of ground troops.
He said it was not usual to announce military dispositions in advance.
"Of course there are circumstances where obviously the air action has to be supplemented by ground forces," he said.
Clear strategy
A Downing Street spokesman said the progress of military operations over the weekend demonstrated that the campaign was on track.
"The strategy is clear and it is working," he said.
"In the first instance, air power has been used to damage Taleban defences, installations, and hitting the al-Qaeda network itself - making the ground more conducive to other operations.
"In terms of overt ground forces - we are in detailed discussion with the US about UK military contribution, but I think in any complex situation we only make announcements when it is appropriate to do so."