MPs had been told to stop leaving sandwiches on their desks and follow other tips after concerns were raised that mice were over-running their offices, with reports also suggesting "mutant super rats" were taking over.
The House of Commons Commission is to consider Battersea Dogs and Cats Home's offer of a rescue cat or two to help with the problem, MP John Thurso said.
Cats have not been used to control the vermin as they can cause serious problems for people who are allergic to them, according to the Liberal Democrat, who speaks on behalf of the commission.
Labour's Diana Johnson (Kingston upon Hull North) had urged officials to use the "traditional" and cheaper method of cats to control pests.
Mr Thurso replied: "My sympathies are entirely with you. I have a perfectly vicious cat (in the Thurso household) which is keeping the rodent population down.
"However, there are serious problems in relation to people who are allergic to cats and to the diseases that cats carry.
"And I can tell you that after an extensive research it is believed that there is no rat problem inside the House of Commons - at least not of the four-legged variety."
Conservative Anne McIntosh (Thirsk and Malton), who recently lost a deselection battle with Tory activists, told Mr Thurso: "We have been offered a rescue cat or two from Battersea Dogs and Cats Home and as I fear I might be allergic to mice and indeed rats of both the two and four-legged variety, I wonder if you would consider this very generous offer from Battersea."
Mr Thurso replied: "I'm sure the commission would want to consider such a generous offer."
Ms Johnson had earlier said to Mr Thurso: "According to recent media reports, mutant super rats are taking over the Commons and it's costing £6,000 per month for vermin control measures on the parliamentary estate.
"Surely the traditional use of cats would be a more effective and cheaper use?"
Tory MP Pauline Latham last month insisted a number of MPs' offices are being over-run with mice.
The MP for Mid Derbyshire said she had returned from the Christmas recess to find the infestation of mice after she accidentally left some food on her desk in her office in Norman Shaw North (building) over the break.
Ms Latham, who used to keep pet mice as a child, said: "I came back from the break to find my desk covered in mice poo and urine. It was disgusting, absolutely disgusting.
"I had left something on the desk which they had shredded. They had obviously been everywhere. They had been living the life of Riley while I was away over Christmas.
"It was awful because I don't want to come in to the office. Some people like to work in the library but I like to have my own space. I just don't want to be here - I am frightened to be here and switch the lights on to see them scuttling away."
A stricter cleaning regime had been implemented, Ms Latham said, adding she had now banned food from her office.