The first incident took place at about 1pm when two men approached the house of an 87-year-old woman on Bankfield Avenue, Heaton Norris on Tuesday 15 October.
They claimed to be officers and forced their way in, went through the woman’s handbag, and left when challenged.
Later, at about 1.30pm, a man knocked on a house on Ingleton Road, Edgeley. He told the 51-year-old woman he was a plain-clothes officer and wanted to make enquiries about security, following a spate of burglaries.
When the woman let the man in, the offender called to someone who claimed to be a colleague. After they looked around and asked questions, the woman challenged the pair who then left empty-handed.
At about 1.35pm, two men approached the house of a 71-year-old woman on Allanson Road, Northenden.
Sergeant Ben Hart from the Force Hub said: “The descriptions given by the victims have differed; however, so while we are keeping an open mind, we are investigating the possibility the offences may be linked.
“These burglaries have distressed those affected and we understand they will concern the communities of Greater Manchester. We are doing all we can to find those responsible.
“We would urge residents to be vigilant and ask that anyone who comes to the door show identification. If you have any doubts, you can ask the person to leave and any genuine professional would understand.”
They claimed to be plain clothes police officers and said that they needed to check security. Searching the house, the offenders stole jewellery and cash.
Anyone with any information is asked to call police on 0161 856 4356 or call the independent charity Crimestoppers anonymously on 0800 555 111.