Ollie Wood and Ethan Hayter have been chosen to compete for GB in Milton, Canada.
Cavendish won silver at the Omnium in Rio 2016 and has reportedly been training over the winter in a bid to secure a place in the British duo for the Madison event in Tokyo.
The 34-year-old, who has been battling the Epstein Barr virus in recent years, competed in the Madison at the 2008 Olympics alongside Bradley Wiggins, but the event was cut from the next two Games.
His participation in the Track Cycling Challenge in December saw him cross the threshold of 250 qualifying points which are needed to qualify for the Olympics. However, he is also required to compete at a counting event - the Track World Cup or World Championships – to be eligible.
The event in Canada is the final round of the World Cup while GB need to be in the top 18 in the world rankings to qualify for the Track World Championships next month. They are currently ranked 20th.
According to The Times, Cavendish’s only chance of making the Games could be by appealing for special dispensation.
Mark Cavendish won silver in Rio
Image credit: Eurosport
His omission from the team might not come as a complete surprise, though, after British Cycling head coach Iain Dyer suggested in December that it would be difficult for Cavendish to make the team as a "Madison specialist".
Dyer told PA: "The door is open but it's extremely challenging to carve out an opportunity at this point.
“When you're travelling to the other side of the world with only five riders at your disposal you really want to make sure you're covered for both pursuits and bunch racing events, ideally with reserves and flexibility there.
“You still want to have five that can ride the team pursuit so to have someone who is solely a Madison specialist in there and doesn't have any other availability isn't the perfect scenario. If one of the other riders goes down you've got a problem.”
Cavendish was a reserve for the team pursuit in Rio but did not feature in any of the rounds.