Extra pest control teams are being drafted in after reports of rats being “displaced” following the fire which engulfed the Glasgow School of Art (GSA).
It is thought that the rodents came up from the drains as fire crews tackled the flames.
“As it becomes clearer where they are being displaced to, we are putting additional pest control resources into the area to get on top of that situation.”
The fire broke out in the historic Mackintosh Building at 11.19pm on Friday and spread to nearby buildings including the O2 ABC venue.
The blaze is the second in four years to hit the art school building, which was undergoing a multi million-pound restoration project to return it to its former glory.
Assistant Chief Officer David McGown, of the Scottish Fire and Rescue Service (SFRS), said: “The investigation into this devastating incident has already commenced.
“Our fire investigation team has started gathering information and, working alongside our police partners, will look at various sources of information to establish exactly what has happened here.
“However, I would like to stress that this is a very complex process and will take time.”
Earlier, Mr McGown told BBC Good Morning Scotland: “I can give this guarantee that we will find out what happened in this fire, what the cause was and what the cause of spread was.”
At the height of the incident, more than 120 firefighters were involved in fighting the blaze.
There have been no reports of any casualties, although emergency services had to evacuate some properties in the area.
The council said 11 people attended a rest centre established in the early hours of Saturday and believes it is possible that other people made their own plans.
Ms Aitken added: “We are conscious that there are people who initially made their own arrangements, or who may have been out of the city at the weekend, who could still need advice or temporary accommodation.”
Tenants are being urged to contact their landlords, while property owners can get help from council homelessness service.
The local authority said it is establishing a Sauchiehall Street taskforce “to manage all aspects of recovery” following the fire, including to support businesses in the area.
The blaze has shocked and saddened people in Glasgow and beyond including leading figures in the worlds of art and music.
Singer Annie Lennox tweeted: “So sad and disappointed for everyone affected by this 2nd devastating fire… (who would believe??!!) at Glasgow’s historic and renowned Charles Rennie Mackintosh art school. .. the renovators, students, staff, alumni, noble fire fighters and everyone in Glasgow.”
Experts have estimated the cost of rebuilding the gutted Mackintosh Building would be at least £100 million, if anything can be salvaged at all.
However GSA bosses said they remain hopeful of a positive outcome for the Mackintosh Building.
Culture Secretary Fiona Hyslop said: “A multi-agency group of conservation experts has been established to advise on short and longer term issues. This group, which includes HES, will continue to play a vital role in the weeks and months to come.
“We are at a very early stage, with the Scottish Fire and Rescue Service still working at the scene. Once a detailed assessment has taken place we will be able to assess any structural, engineering or other work required.”
Meanwhile, Labour MP for Glasgow North East Paul Sweeney, who is director of the Glasgow Building Preservation Trust, said that having been escorted round the building by SFRS, it is clear the interior is almost entirely lost but the main structural beams appear to still be largely intact, giving hope some of it can be saved.