The 25-year-old currently plays his club football in Mexico with Pachuca.
He only left his homeland in January to take on a new challenge in North America, but has opened the door for another move to be made.
Several clubs are reported to be weighing up an approach after being impressed by his performances before and during the World Cup.
He plundered three goals in as many pre-finals warm-up games, including one in a 2-2 draw with England in Miami.
With his confidence soaring, Valencia then netted in Ecuador’s opening fixture in Brazil against Switzerland and bagged a brace in a 2-1 victory over Honduras.
Teams in Spain are now reported to be leading the chase for his signature, with Espanyol among those looking to acquire the services of a proven goalscorer.
Valencia told TV Azteca on his hopes for the future: “It would be a good moment to move to Europe, after what I have done in Mexico and at the World Cup.
“I really like Italian football but if this jump to Europe happens, I will welcome it and try to do my best wherever I go.”
Pressed on reported interest from La Liga, he added: “These are the best leagues in the world.
“If there is an opportunity to move to one of them, you have to do it.”