Valverde has led los Che to sixth in La Liga where they find themselves in contention for European football next season, despite financial problems at the club.
The 49-year-old has been linked with a move away from the Mestalla stadium, but has admitted sporting director Braulio Vazquez has been talking to his representatives, with his contract set to expire at the end of the season.
“Braulio has spoken with my agent, and with other people. But there is no further news,” he told reporters.
“As soon as I know who the president will be, I will talk to him on the same day. Until the date of June 4 we will not know who it is, but as soon as I do, I will sit down with him.”
The direction of the team will be a huge factor in whether Valverde will continue his reign at Valencia, with economic worries forcing the club to look at the youth element for fresh players.
“The theme of the arguments, in my opinion, has to start from a belief and not an obligation. You have to think in the long term," he continued.
“And not because we are in a bad economic situation that we have to look to the youth team. There will be some that can move up to the first team and others that won’t.”
Valverde's charges face Osasuna this Saturday when they will be continuing their push for Europe.