The midfielder was left out of the Athletic side which succumbed to a 3-1 defeat to Real Madrid on Sunday, prompting speculation that the Basque side could be prepared to cash in on the 24-year-old, but Valverde maintains he does not expect any business to be conducted before Monday's deadline.
"It had nothing to do with the bid from Manchester United, I left him out because I chose the players I thought were best suited to the game," he said after the match at Santiago Bernabeu.
"I'm not thinking about speaking to him to convince him about anything and I'm not worried about anything else.
"I haven't spoken with the player but what I'm going to repeat is that I don't expect the club to make any moves in the transfer market tomorrow.
"I do not know what will happen. I want Ander to stay with us, and that is what I think, what I expect will happen."
Meanwhile, team-mate Ibai Gomez has revealed that Herrera has told the squad he is happy to stay at the club.
"Ander told us that Athletic is his club and, at the moment, he is staying here," he told Gol TV.