Officers discovered the dismembered woman at a house in Peterborough, after tenants complained of a smell coming from one of the rooms.
The room in question was previously occupied by Lithuanian Vitautas Jokubauskas – who police have confirmed as a suspect.
Officers are also concerned for the safety of Mr Jokubauskas' girlfriend.
She is also thought to be Lithuanian and aged around 40 with dark hair.
It is believed that Mr Jokubauskas has fled to Eastern Europe or Ireland, and Detective Chief Inspector Adam Gallop said: "We are very keen to trace [him] and we are clearly very concerned for the welfare of his partner, who hasn't been seen for some time.
"Investigations are ongoing to determine where this murder took place and our priorities are to locate Mr Jokubauskas and identity the body.
"I would urge anyone who thinks they have seen Mr Jokubauskas or recognises the description of his partner to contact the police as soon as possible. Anyone who sees him should not approach him and should contact police immediately."
If you have any information relating to this crime, you can contact the Major Crime Unit on 101. Alternatively you can speak to Crimestoppers on 0800 555111.