Neville, who was appointed coach until the end of the season in December, faced an uncertain future amid three consecutive defeats but the Englishman has overseen a change of fortune at Valencia.
Valencia completed a 10-0 aggregate win over Rapid Vienna to reach the Europa League last 16 via a 4-0 victory on Thursday, taking the club's undefeated streak to five matches in all competitions.
And as Valencia aim to win a third successive La Liga fixture, when they meet Athletic Bilbao on Sunday, Neville said: "I haven't spoken to the club about my contract.
"We originally said March but March is almost upon us and we need to focus on the next games. Now's not the time. We'll leave it until April.
"I can assure you that there have been no discussions yet."
Of the fans who had called for Neville's sacking earlier this month, the former Manchester United captain added: "I hope that they think I am a sincere and hard-working person. I want them to think that I give my all every day.
"When I was younger, the only thing I wanted from my team was that the players would die for the club, feel the shirt... and that's what I want them to think when they think about me. After the 7-0 [loss against Barcelona in the Copa del Rey] I felt that pain. Now we have won four games on the trot.
"It was the players and the fans who won the Espanyol game and they are the most important people at this club."
Valencia are 12th in the league with 31 points following back-to-back wins against Espanyol and Granada.
"Obviously we are going into the game with confidence, the confidence you get from winning matches, working hard in training and preparing ourselves well," Neville continued.
"A few weeks ago, I wasn't looking at the league table, nor am I looking at it now. I think we are in a good moment."