Instead, the 32-year-old is competing for the Barisal Burners in the Indian Premier League.
Cook believes that it is up to each player to decide on their own priorities but said for him, and many others, Test cricket comes first.
"Quite clearly I believe that Test cricket is the pinnacle," said Cook. "I still think most players believe that too.
"Twenty20 has done wonderful things – the numbers of kids playing has gone up, the number coming to watch game has gone up. So it's been an important thing for the game. But we need to manage things well to protect Test cricket.
"Clearly financially it makes a lot of sense to play Twenty20 cricket — you can't begrudge players doing that. So that's why it comes back to those running the game to ensure when Test cricket is played it is the best two available sides facing each other."
The first Test gets underway at Lord's on May 17.