Cabinet members will be asked to approve the investment when they meet on Wednesday.
All council properties are already fitted with smoke alarms, but this scheme will see additional alarms being installed to ensure there is one on every floor of every property where there is living space.
It is in preparation for the government’s new Smoke and Carbon Monoxide Alarm (Amendment) Regulations 2022, which comes into force on October 1 following the review.
In the Grenfell fire, it was revealed that none of the 120 fire doors to the flats - 106 of which were replaced not long before the fire - were compliant with regulations.
In addition, fire doors onto the stairwells were also broadly non-compliant, and in some instances ended up being propped open by a fire hose.
A cabinet report said: “There are no alternative options - this is a regulatory requirement.
“Following the tragic events of Grenfell and the focus on building safety, the government held a consultation on the proposal to extend the requirements for smoke alarms and carbon monoxide alarms into the social housing sector in line with Scotland.
“This consultation took place between November 2020 and January 2021.
“In order to comply with the new regulations, Berneslai Homes will have to work at speed to install the remaining alarms by October.
“The council has requested a monthly update on installations and a copy of the process which deals with no access and refusal issues.”
There will also be additional carbon monoxide alarms installed at Berneslai Homes-run properties with fires and boilers, but this won’t apply to properties which have gas cookers only.
Coun Robert Frost, cabinet spokesperson for regeneration and culture, said: “All our properties already have smoke alarms, and Berneslai Homes had already begun installing additional alarms to cover multiple floors.
“We’re now asking cabinet to approve this extra investment to accelerate this programme so we can complete it before October 1 when new regulations come into place.
“I encourage all tenants to work with Berneslai Homes to make sure their teams can access properties to complete this work as soon as possible.”
According to the report, an estimated 31,467 extra items will have to be installed, made up of 18,167 smoke alarms and 13,300 carbon monoxide alarms, costing £2.83m.
Dan Crossley, head of repairs, maintenance and building safety at Berneslai Homes, added: “Keeping tenants safe is our number one priority, so we welcome the additional investment to install these alarms which will help keep tenants safer in their homes.”