De Gea is out of contract next summer after United triggered a 12-month extension on his deal.
The club are keen to tie him down to a longer deal though following plenty of speculation that he would be willing to leave Old Trafford.
De Gea is believed to currently earn £210,000 per week at Manchester United, though he wants more.
The shot-stopper has told United chiefs that he is prepared to commit his future to the club, but only if the price is right.
Express Sport understands that to be £350,000 per week to make David de Gea the highest-paid goalkeeper in world football.
United executive vice-chairman Ed Woodward has seen a number of players sign new deals in recent weeks under Ole Gunnar Solskjaer.
Phil Jones was the latest to put pen to paper when he extended his United deal on Friday.
Anthony Martial, Luke Shaw and Chris Smalling have all signed new contracts recently too.
Solskjaer has led United to ten wins out of 11 in all competitions, with the latest being a 3-0 victory at Fulham.
De Gea was hardly tested at Craven Cottage, but has impressed in recent weeks.
He is among the best goalkeepers in world football currently and is earning praise from some United fans, who hail him as the best the club has seen.
Danish star Peter Schmeichel and former Fulham hero Edwin van der Sar both shone during their time at Old Trafford.
And Solskjaer believes De Gea is competing with that pair for United’s best ever goalkeeper.
“We’ve had some great keepers at this club and I think he’s challenging both Edwin and Peter for the number one spot historically,” Solskjaer recently said.
De Gea has won United’s player of the year award in four of the past five seasons.
He is set to be back in action as Manchester United host PSG in the first leg of the last-16 of the Champions League on Tuesday (8pm).