The 27-year-old will remain at the club until the end of the 2019-2020 season, as United will invoke their option to extend his current deal by a year at the end of the season.
However, convincing the Spaniard to stay beyond that looks increasingly unlikely for the club, who are in the grip of a crisis.
The keeper's reluctance means that United face the unappealing choice of letting him leave for nothing in 2020, or cashing in before then.
De Gea has been named United's Player of the Season in four of the last five seasons, and he has been in impressive form so far this year.
His reluctance reportedly stems from United's inability to challenge for the top honours domestically and in Europe.
With manager Jose Mourinho's future in doubt, the keeper also feels unwilling to commit his future to a club in the midst of such uncertainty.
De Gea's agent, Jorge Mendes, met with United representatives in London on Friday, but they were unable to come to terms over a new contract
De Gea previously came close to joining Real Madrid, but the move broke down on deadline day in the summer of 2015.