An accord between the clubs following last season's failed transfer deadline day transfer, which would have allowed Real to come back in for the player this summer for 35m Euros plus extras, expired on June 15.
Now Real coach Zinedine Zidane has informed the club he is happy with the form of current keeper Keylor Navas and does not see the signing of De Gea as a priority.
The news is a relief for United who are desperate for De Gea, who signed a new contract after his move to Real collapsed, to stay at Old Trafford.
New manager Jose Mourinho has already spoken to the player to explain his project.
A source close to the player said: "David had no doubts about staying. Now the challenge is to win the Premier League with Mourinho at United."
De Gea is currently with the Spain squad at Euro 2016 and due to face Croatia in Bordeaux on Tuesday.
