However the former Barcelona goalkeeper conceded that Real Madrid, who are expected to sign the Spain international this summer, are one of three clubs every player wants to play for along with United and Barca.
Valdes made his Manchester United first-team debut after De Gea limped off injured during the second half against the Gunners - but the latter gave little away, with regards to his body language, about his future plans.
Asked whether De Gea's post-match wave was a clear sign the Real Madrid target plans to leave Old Trafford, Valdes was quoted by the Mirror as saying: “I don't know, you have to ask David about that. I can't answer that.
"[But] Madrid, Barcelona and United are three of the biggest clubs in the world. Everyone in the world wants to play for these clubs.
“It's a question you would have to put to David. I cannot answer for him. I am very happy to be here. I have one more year on my contract here. Let's see what happens.”
Real Madrid expected to make their move
Real Madrid have been surprisingly coy about De Gea over recent weeks and month, but the reigning European champions are expected to make an official move for the 24-year-old once the season finishes.
Iker Casillas's best years are now firmly behind him, while Keylor Navas has failed to make the impact many expected he would following his summer move from Levante.
Real Madrid are in need of a new world-class goalkeeper and De Gea, who was born and raised in the Spanish capital and only has 12 months left to run on his contract at Old Trafford, ticks all the boxes.
De Gea appears to have made up his mind
That De Gea has refused to sign a new contract with the Red Devils, despite being offered a staggered £200,000-a-week deal, suggests the agile shot-stopper has already made up his mind to leave his current employers.
But the Manchester United faithful gave De Gea some food for thought by chanting his name throughout the game against Arsenal.
Whether that will have any bearing on his final decision, though, is doubtful - and it would be a surprise if De Gea is not a Real Madrid player by the first weekend of the 2015-16 campaign.
Is Victor Valdes the perfect replacement for David de Gea? Have your say in the comments below!