With just 18 months remaining on his contract, De Gea has been linked with a transfer to Real Madrid but on Sunday night, manager Jose Mourinho talked up the need to keep the Spaniard at Old Trafford.
United will trigger a 12-month option in De Gea's existing deal - effectively meaning that he is contracted to United until 2020 - but according to The Mirror, the Premier League giants are willing to give 27-year-old the chance to remain in the North-West of England for the remainder of his career.
Reports have previously suggested that De Gea would like a return to La Liga at some stage in his career, but United are willing to increase his wages to £250,000 per week.
De Gea may be prepared to bide his time over fresh terms due to his current agreement with United, but it appears that the club's hierarchy has signalled their intentions to keep him in the long term.
Since joining from Atletico Madrid in 2011, De Gea has made a total of 296 appearances in all competitions.