The pandemic has led to a surge in the number of cats being taken with data showing thefts were up three times in five years.
Compulsory microchipping for cats and kittens aims to help reunite thousands of owners with their lost or stolen pets.
The microchipping measure, which means animals can be tracked and identified if they are stolen or resold, is part of a raft of measures to combat the black market in stolen pets.
Those who refuse to microchip their pets will face fines under the proposals, the Telegraph reports.
The taskforce was set up by Robert Buckland, the justice secretary, with Priti Patel, the home secretary, and George Eustice, the environment secretary.
As it stands an estimated 2.6 million cats are not chipped in the UK.
Microchipping is a painless insertion of a chip under the skin and it helps owners find their pets if they go missing.
A government spokesperson said: “Last month the home secretary, the lord chancellor and the environment secretary met to discuss a cross-government approach to combatting this issue and we will announce next steps in due course.
“This builds upon the huge amounts of work already undertaken by junior ministers and officials to address this cruel and criminal practice.”