The bodies of a man and a woman were discovered at around midday at a building in Ness Grove, Cheadle, which has been sealed off.
Forensic experts were working at the scene and police said a thorough investigation was under way.
A spokesman said: “Officers were called to the property at approximately 12:50pm after two bodies had been found inside, those of an adult male and an adult female.
“At this stage the deaths are being treated as suspicious and the property has been cordoned off.
“A detailed forensic examination of the scene is under way.”
Police will continue to carrying out house-to-house inquiries today. Anyone with information which could assist the inquiry is asked to contact Staffordshire Police.