The Spanish goalkeeper, who is out of contract at the end of the season, could reportedly sign a deal worth up to £300,000-a-week.
Jose Mourinho insisted that De Gea wants to stay with United following Tuesday's narrow win over Young Boys.
But the 28-year-old, who has been with the club since 2011, is yet to put to paper.
Manchester Evening News have reported two key factors that are helping him to make his decision.
The ex-Atletico Madrid star has allegedly felt moved by the ongoing support from loyal United fans.
And his girlfriend, Edurne Garcia, gave him another reason to stay when she relocated to Manchester.
The 32-year-old, who previously lived in Spain, once famously claimed that Manchester was "uglier than the back of a fridge."
According to the Standard, club chief Ed Woodward knows De Gea's new deal will have to make him one of the team's highest earners.
But a £300,000-a-week contract would still leave him behind Alexis Sanchez, who pockets £350,000-a-week, in the pecking order.
If he does not sign a deal with the Reds, it is understood that the club will slap him with a whopping £75 million price-tag.
Juventus emerged as early favourites, with French giants Paris Saint-German also showing interest.
Following his impressive display against the Young Boys, Mourinho branded him as the best goalkeeper in the world.
The United boss said: "You know he's a world class player, he's the best goalkeeper in the world.
"If our ambitions are to be a big club to be a winning club you need the best goalkeeper in the world and you need also some other players that are the best in the world."
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