CONI said in a statement that it had written a letter of intent to the International Olympic Committee (IOC) putting forward the two northern cities as potential hosts.
It added that a feasibility study had already been carried out and would be handed to the new Italian government when it is eventually formed, this month's election having produced a hung parliament.
Turin staged the Winter Games in its own right in 2006.
Sion in Switzerland and Stockholm have also expressed interest in the Games as well as cities from Austria, the United States and Canada, among others.
However, one Austrian city, Innsbruck, abandoned its plans to bid after they were rejected in a referendum.
The 2026 bidding process is in the so-called "dialogue phase" which the IOC says allows potential hosts "to explore the benefits of hosting an Olympic Games."
The IOC session in October will invite candidates to formally bid, with final a decision on hosting rights to be taken in September 2019.
The bid process has been overhauled after a string of cities pulled out in previous bids, fearful of the Games’ cost, size and environmental impact.
Rome was among four cities which pulled out of the process to host the 2024 summer Olympics.
(Writing by Brian Homewood in Bern, editing by Pritha Sarkar)
