The current Athletic Bilbao boss did previously play for Barcelona and guided Espanyol to the 2007 UEFA Cup final as manager.
Sport say the signing of the midfielder would have Valverde's "complete and total support" and that he was never happy the Basque club sanctioned his sale.
However, when asked about the reported interest from the Catalans, he told a news conference on Wednesday: "I can not confirm it, I'm sorry". "I have an agent and there are teams that have shown interest in me".
"I can't decide myself on anyone and I don't know who will be the next manager. It doesn't depend on what Real Madrid do, I just think we can aspire to much more".
Former Barcelona player Valverde, 53, steered Athletic to eighth place in the Primera Liga this season, but has made a decision to call time on his second managerial stint at the San Mames. "This wouldn't be the first time that I have offers from important clubs".
"Right now I have no commitment to any team even though there are teams that have been interested in me", he said at a press conference to confirm his Bilbao departure.
"I feel my work here is done", Valverde said.
He then led Olympiacos to three league titles and two cups, and helped Bilbao win the 2015 Supercopa de Espana against Barca. "I never talk about negotiations with clubs and that won't change".