The 18-year-old was dragged from a bus stop in Beeston and bludgeoned with a stone before being sexually assaulted.
Police have already visited 1,000 homes and taken swabs from 250 men since the attack on 6 March.
Officers are testing anyone broadly fitting the description of the offender.
Det Supt Nick Wallen, of West Yorkshire Police, said: "The offender's movements on the night of the attack strongly suggest the attacker has a link to the Beeston area.
"This mass swabbing operation is just one aspect of the investigation but it is vitally important for us to be able eliminate as many potential suspects as possible.
"The fact that we have a full DNA profile for the offender means that nobody has anything to fear about being wrongly implicated or telling us about anyone they have suspicions about."
Detectives previously released images and a description of the attacker, who is thought to be in his early 20s and of Pakistani or Middle Eastern origin.
On the night of the attack, he was wearing a green Puma hooded top and white trainers.
An image of a footwear mark recovered from the victim's clothing has now been released and is thought to be from a Nike 'Huarache' shoe.
"These types of trainers are mass produced and widely available, but I would ask people to consider it alongside all the other elements of description and consider whether it points to a particular individual," Det Supt Wallen said.
It recently emerged three other women were stalked by the suspect prior to the attack on Beeston Road.
Police have warned women on the city to be on their guard.
Detectives investigating the rape and attempted murder of a woman in Leeds are conducting a mass DNA swabbing operation in the hunt for her attacker.