Wales hopes to follow Scotland, who are hosting the 2014 Commonwealth Games in Glasgow.
Chris Jenkins of the Commonwealth Games Council for Wales said no decision has yet been made but the work has begun on the feasibility study.
The Welsh Government is currently working with Cardiff Council and other important stakeholders.
The Welsh Government said: “We have made a commitment to work with Cardiff City
Council to look at the feasibility of bidding to host the 2026 Commonwealth Games.” The Commonwealth Games Council for Wales is working with the Commonwealth Federation.