"I can't decide myself on anyone and I don't know who will be the next manager".
Former Barcelona player Valverde, 53, steered Athletic to eighth place in the Primera Liga this season, but has chose to call time on his second managerial stint at the San Mames.
The Catalans are on the hunt for a new boss with current manager Luis Enrique to vacate the hot seat after Sunday's Copa del Rey final, where Barca will face Alaves.More news: Mickelson to miss US Open for daughter's graduation
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Asked about Barcelona's reported interest in signing him, he said: "I can not confirm it, I'm sorry".
"But I have an agent and I'm not going to deny that some clubs have expressed interest in me", Valverde said in press conference on Wednesday 24 May.
Sport reports that the 53-year-old has already discussed transfer targets with Barcelona's hierarchy and instructed them of his desire to sign Herrera, who turned in a man-of-the-match performance against Ajax last night.
New Balance has taken over as official kit supplier for Spain's Athletic Club (also known as Athletic Bilbao). It's not the first time there have been offers from big clubs. He spent six years with Athletic from 1990-96. This season Athletic Bilbao finished seventh in the league, one point behind Basque rivals Real Sociedad. He also coached the club from 2003-05.