The 25-year-old striker has scored three goals in Ecuador's opening two matches at the tournament, leading to speculation that Newcastle United, Everton and Tottenham Hotspur could all be lining up a move.
Club president Andres Fassi told ESPN Mexico: "Enner Valencia's value increases every day. We don't know if he will stay, it will be hard given the offers we have received.
"The options that a great player at this level gets are to be taken into account. But for now he has to keep doing things right.
"No doubt it would hurt us to let Enner Valencia go, but we are realistic about his quality. I don't want to name a team, we want to respect the sporting moment of the player and of his national team."
Valencia will be in action with Ecuador again on Wednesday when they face France at the Maracana.