Ticket to Ride Europe: Drawing destination cards
Destination tickets are kept secret until the end of the game and the final scores are counted. You can't start the game with no cards, and you can never discard the ones you keep, so there is no way to hold zero destination tickets at any point in the game.

This is written on the last page of the Ticket to Ride rules, the last paragraph under "drawing destination tickets".


  Destination Tickets are kept secret from other players until the Game's final scoring. A player may have any number of Destination Ticket cards during the game.


http://cdn0.daysofwonder.com/tickettoride/en/img/tt_rules_en.pdf