The Spain international has long been linked with a switch to Real Madrid, having previously represented city rivals Atletico Madrid.
De Gea came close to joining Los Blancos in 2015, only for an administrative error on deadline day to thwart the move.
The 27-year-old went on to sign a new four-year contract in September of that year, with the option of a further 12 months.
According to the Manchester Evening News, De Gea is now set to end speculation over the purported switch to Real once and for all by committing his future to the Red Devils.
The Madrid-born custodian has spent the last seven years in the North-West of England, making a total of 315 appearances in all competitions.