The event was due to take place in Nice in southern France on 14-18 September but did not happen due to security fears after July's lorry attack in the city, which killed 85 people.
Brittany, in north-west France, is also being considered.
Yorkshire hosted the Grand Depart for the Tour de France in 2014.
Organisers of this year's Tour de Yorkshire have said more than a million people turned out to see the race.
Representatives from Yorkshire are in talks with the European Road Cycling Union to host the recently cancelled European Road Cycling Championships.