When the man asked for his solicitor and was asked what their phone number was, her replied: ‘I have no idea.’
Two men had climbed onto the roof of the house at Walton Breck Road in a bid to escape Merseyside Police at around 6.30pm on Wednesday.
One of the men was later arrested by officers on suspicion of possession of Class A and B drugs.
However, the second man, who is wanted by police, remained on the roof for the rest of the evening.
Police placed a cordon on Walton Breck Road between Sleepers Hill and Everton Valley, as Merseyside Fire and Rescue Service and the North West Ambulance Service rushed to the scene.
The man was seen walking along a number of roofs on the road and at one point almost slipped and fell, the Liverpool Echo reported.
He also shouted to the crowds of people who gathered on Sleepers Hill and Paley Close and told them he wanted to speak to his solicitor.
But when one woman asked what the number was, he said "I have no idea".
He then asked for a double pepperoni pizza as he sat beside the chimney of one of the houses and told those gathered below that he had plenty of cigarettes and would not be coming down.
A spokesperson from Merseyside Police said they had received a report that a wanted man had been sighted with another man in the Sleepers Hill area.
"Patrols attended and the men were located on the roof of a property on Walton Breck Road,” police said.
“It was reported that one of the males had discarded white and brown rocks (suspected drugs).
“One of men came down from the roof, was detained by police and arrested on suspicion of possession of Class A and B drugs.
"He will be taken into custody and questioned by police. The second man remains on the roof and officers are at scene attempting to engage with him."