The attacker, known as the Bath Rapist, is thought to be responsible for attacks and other attempted abductions dating back to May 1991.
Officers plan to take swabs from all the men whose names have come up during the course of the investigation to test their DNA.
The case is the UK's longest-running serial rape investigation.
Detective Inspector Paul James is leading the manhunt and he told BBC Radio Bristol: "It's very simply a question of going round and seeing these people and asking them to provide us with a DNA sample, which obviously we can test against stuff we have in our possession."
He indicated that in similar DNA testing programmes, individuals had rarely refused to give a sample.
"It may well be one of the people that's in our system that we are now going to visit could well be the offender.
"It's equally possible he's not in our system yet."
News of the DNA testing coincides with a fresh appeal for witnesses on BBC1's Crimewatch programme on Wednesday.
Police determination
DI James, from Avon and Somerset Police, said: "I'm asking the people of Bath to think again, to look at this new information and to tell us who this man is."
"We are more determined than ever in our hunt for this offender."
In most attacks the man has targeted woman in their cars, often driving them to a secluded area to be raped, then bringing them back to where he found them.
Some have been forced to wear tights and were blindfolded with a hairband.
Scar
The rapist is described as white, slim, in his 30s, between 5ft 8in and 5ft 10in tall, with distinctive blue eyes and a scar below his bottom lip.
He is said to wear black clothes and a baseball cap with a batman logo on it during the attacks.
Police say he has an extremely good knowledge of the area and has committed offences one after the other on the same night.
Often there is a big time gap between the assaults. Detectives believe this could be a clue to the man's identity.
They say relationships he may have been in could have ended, or he could live or work away from the area, returning only sporadically when he strikes again.