The incidents have been reported to trading standards, the council and the police.
A Rushcliffe Borough Council spokesperson said: “The Council is aware of reports of individuals knocking on doors on February 27 in Compton Acres and Gamston selling insulation for homes and completing welfare checks on residents, claiming to be from the authority.
“We can confirm no teams from the Council are conducting this work. We have raised this with Nottinghamshire Police and Trading Standards and would encourage all residents to not engage with anyone on the doorstep, making similar claims.
“Any further instances should be reported to Police on their non-emergency number 101.
“It is important that we encourage family, friends and neighbours to speak to the elderly and vulnerable in their community and ensure they thoroughly check the ID of those knocking on their door. If they are unsure at all, they can call the Council to verify on 0115 981 9911.”
Rushcliffe Inspector Craig Berry added: “We are working closely with the local council in relation to these reports of people knocking on doors last week in the Compton Acres and Gamston areas and purporting to be council officials.
“We want to remind people to be on their guard, especially if someone you’re not expecting – a man, woman or even a child – knocks on your door.
“Don’t allow anyone without valid identification access to your home and, if you’re unsure, don’t let them in. Keep the chain on the door while talking to them and check with the company that the person is purporting to be from.
“Our advice is always to say no to cold-callers and to report any suspicious activity. If you see somebody acting suspiciously report it to the police immediately by calling 101 or, in an emergency, call 999.”