Although he said that all supposed information about an early departure was just speculation, McAllister also revealed, "An official announcement of the British forces with possibly new withdrawal dates is anticipated for January 2013."
An internal note from the British military recently caused waves after it suggested that troops would be leaving Lower Saxony bases at Fallingbostel and Bergen in 2015, with the process complete by 2018 - a full two years before what had previously been expected.
"These papers describe possibilities for consideration, but are not definitive," McAllister said.
He has been to London to discuss the withdrawal of British troops with UK Prime Minister David Cameron. He has appealed for the decision not to be unnecessarily delayed.
"We hope for clarity as soon as possible over the withdrawal of British troops," said McAllister, adding that he hoped that Lower Saxony would not be completely shorn of a British military presence.
Thousands of local jobs are considered to be at risk when the British troops, their families and support staff leave Germany. Yet the plans to leave are expected to save the British defence ministry millions of pounds a year.