The fresh offer is worth £350,000 a week for the four-time United Player of the Year, who has been the standout performer post-Sir Alex Ferguson.
A signature across the dotted line would pin De Gea to United for four years, with the club holding an option to extend for another year.
Although the 28-year-old’s head has been turned in the past, notably by Real Madrid who almost signed him in 2015, he now wants to stay in Manchester.
Ole Gunnar Solskjaer revitalised the side when he first arrived, with De Gea lauding his manager after a virtuosic performance in a 1-0 away win against Tottenham in January.
Man Utd transfer news: David de Gea wanted to rival Alexis Sanchez's staggering wages (Image: Getty)
He feels Solskjaer can bring back the emblematic characteristics of United which have faded since Ferguson retired in 2013.
The report also states De Gea could wait to see how the club’s summer business unfolds before staying, though.
The shot-stopper is not as hot a commodity as this time last year with a poor World Cup denting his confidence, which showed at times last season.
De Gea made four errors leading to goals in the 2018/19 Premier League campaign - he had made six in seven seasons leading up to that point.
Man Utd transfer news: David de Gea wants to stay despite a poor end to the season (Image: Getty)
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I don't think United should be held to ransom just because they have this wealth.
Andy Mitten, United We Stand editor
Those blunders turned off Real Madrid and Paris Saint-Germain, who were the most likely suitors.
United We Stand editor Andy Mitten told Sky Sports’ Transfer Talk podcast in May: “I don't think United should be held to ransom just because they have this wealth. They are already overpaying for under-performing players.
“De Gea is not an under-performing player, he has been the player of the year for four of the last six years, but there are levels and he has been offered a deal to become the best-paid goalkeeper in the world and it's not enough.
"I don't think United should just succumb to every agent's demands just because the fans are saying: ‘Pay him whatever.’ You can't just do that."