Officers were alerted to suspicious activity and attended a premises off Allport Street at 9pm on Monday.
A man, aged 33, and a woman, aged 52, both from the London area, were arrested on suspicion of remaining in the UK beyond the legal limit.
The woman was also arrested on suspicion of permitting the use of a premises as a brothel, while the man was arrested on suspicion of keeping a brothel.
Both remain in custody while enquiries continue.
A spokesman for Staffordshire Police said: "Anyone with any information should contact Staffordshire Police on Facebook, Twitter, or call 101, quoting incident 629 of 17 January.
"Alternatively, contact Crimestoppers anonymously on 0800 555 111."