The report suggests that, despite interest from Barcelona, De Gea will put pen to paper on a new long-term deal in the coming days that will tie him to the Old Trafford club until 2018.
Drayton quotes a source as telling The Sun (subscription required) newspaper: "David is happy in the Premier League and knows this is the season to really show what he can do. As for Barca, it'll be tough for them to convince United to sell."
A new deal would complete a remarkable 12 months for De Gea, in which he has overcome competition for his place in the Manchester United first team and go on to be named in the PFA Premier League Team of the Year.
The Spaniard, 22, is now United's established first choice and has been in fine recent form to help his team through what has been a tough start for new manager David Moyes.
In particular, one spectacular save in last weekend's fixture with Sunderland proved a real turning point in the match. De Gea prevented the Black Cats from taking a 2-0 lead in a game that United came back to win 2-1 at the Stadium of Light.
Per the Daily Mail's Thom Drake, De Gea's former goalkeeping coach at United, Eric Steele, recently spoke to the United We Stand fanzine about the player's initial issues at the club.
Steele blamed a lack of focus in training and a poor diet for some of De Gea's teething problems in English football.
However, the changes the pair made to the player's regular routine have proved a major success, with the former Atletico Madrid keeper now a much stronger and more confident player when dealing with aerial balls lofted into the penalty area.
De Gea finished last campaign in double figures for clean sheets, earning the plaudits of his peers at the PFA's end-of-season gala.
Steele has now moved on, with manager David Moyes bringing Chris Woods with him from Everton to act as United goalkeeper coach. His legacy in terms of the improvement in De Gea's all-round play, though, looks set to be visible at Old Trafford for some time yet.