Neighbour Maureen Cooper reported seeing police activity at Moazzam Begg's house in Hall Green from about seven o'clock.
She said a number of unmarked vehicles had arrived, one of which appeared to contain photographic equipment.
A small silver car and a green people carrier were taken away on low loaders, she said.
She also said Mr. Begg's wife had told her in a conversation last autumn that he had been abroad for "several months."
More top news
D-Day veterans from the West Midlands were given France's highest honour today, 18 months after a pledge to award every living soldier.
Dry for much of the Wednesday with possible brighter spells in the east. Outbreaks of rain will spread southwards later in the day.
Wednesday will be another rather cloudy and mild day. Although dry for most the odd spot of drizzle is possible, mainly over high ground.