Valverde fearful over Herrera departure
Herrera was an unused substitute in his side's 3-1 defeat to Real Madrid on Sunday, fuelling speculation he could set for a move to Old Trafford.
Athletic Bilbao president Josu Urrutia confirmed on Friday that the club had turned down an initial bid for the player, worth €30 million, but the Premier League champions are expected to return with another offer.
Asked about Herrera's potential move, Valverde said it was "such a worry", adding: "We will see tomorrow because tomorrow (Monday) the transfer window is closing. I haven't spoken to the player.
Valverde admitted that it would be "more difficult" to envisage Herrera remaining at the club than joining the Premier League champions, but insisted a deal was not done, and his decision to leave the player on the bench was based on football motives.
"There is nothing related with United. I wanted to play with another players," he said.
"If he (Ander Herrera) had something with United he wouldn't have been on the bench because we had 19 players (in the squad).
"I think it would be more difficult to explain the contrary (Herrera going to Manchester United). I think it's the normal thing.
"The strange thing is a club (reportedly willing to pay) €36 million for a player. It doesn't happen every day, either 36, 20 or 25. I don't know. Maybe here in Madrid they are used to that. In Bilbao not."
Bilbao had won both of their La Liga fixtures this season before their trip to the Spanish capital, but an Isco double and a Cristiano Ronaldo goal saw them slump to a 3-1 defeat.