The former Manchester United defender is keeping the seat warm for the Premier League title winner, according to The Sun.
Under-pressure Mourinho is Peter Lim's top target to take over at the Mestalla at the end of the current season.
Neville is also the favourite to become the new England manager after Euro 2016 after working alongside Roy Hodgson as a coach throughout the qualifying campaign.

An influential Spanish source told: "Many in Valencia believe Mourinho will come here next summer with Neville returning to England."
Jorge Mendes, Mourinho's agent, has close ties to Lim and the Spanish club, which could play a pivotal role in any move for the Chelsea boss.
On being appointed as the new Valencia head coach Neville said: "I am absolutely thrilled to be given this opportunity with Valencia.