"They are in retreat, they are moving out," said Rambukwella, who is also a government minister. "Their presence is not felt."
The fall of Kilinochchi would be devastating to the Liberation Tigers of Tamil Eelam (LTTE).
The town has little military importance but it is seen as one of the most significant symbols of the rebels' decades-long fight to create an independent state in the north and east of Sri Lanka.
News of the imminent capture of Kilinochchi comes as Velupillai Prabhakaran, the rebel leader, prepares to deliver his annual speech to the Tamil people on Thursday.
The speech marks "Heroes' week", an annual event when the rebels commemorate the estimated 22,000 Tamils who have died during the 36-year-long war.
The Tamil Tigers once controlled a large de facto state in northern Sri Lanka but have been forced into a rapid retreat by a massive military offensive.
The military forced the rebels to abandon their strongholds in the east in July 2007 and the government has vowed to end the war by the end of this year.