He is being assessed by psychiatrists who are to report to the Prison Service recommending he be moved to Broadmoor Hospital, Berkshire.
A source said: “Adebowale is on a variety of medication to control his psychotic episodes.
“The drugs are quite strong and make him pretty spaced out. He sometimes resembles a zombie.
“He spends most of his time either in bed or sitting on it and rarely ventures out of his cell.
“He is being assessed by psychiatrists who have to decide whether he is mentally ill.
“The strong feeling is that he will be moved to Broadmoor within the next few weeks.
“He really needs specialist care.”
During one psychotic episode, Adebowale told officers he did not believe in the Koran and had reverted to being a Christian.
He also refused to speak to accomplice Michael Adebolajo, 29, when they were caged in the same super-secure unit.
The pair were convicted by an Old Bailey jury last month of murdering Fusilier Rigby, 25, last May.
Originally, they were in a unique unit – a prison within a prison – at the category A jail.
But the Daily Star Sunday can reveal they ordered their lawyers to push for lower-security cells.
They were eventually moved to another segregation block.
The killers were allowed out of their cells to pray to Mecca up to seven times a day.
The source added: “They were treated with kid gloves and it angered staff who had a very difficult job to do.”
Five prison officers remain suspended after Adebolajo accused them of assaulting him.
The Crown Prosecution Service has said there will be no charges.
But the officers – dubbed the Belmarsh Five – are still suspended while an internal investigation is conducted.
They deny any wrongdoing.
Steve Gillan, general secretary of the Prison Officers Association, said: “We fear they could be victims of a witch hunt.”
