It is understood the Manchester United goalkeeper, 28, is close to signing a new £350,000-per-week contract at Old Trafford.
But according to ESPN, the club are concerned that his agent is driving up the price of the deal, inflating their client's wages.
However, United believe they can still match the demands from their four-time Player of the Year.
De Gea is represented by Portuguese firm GestiFute, the agency set up by super-agent Jorge Mendes.
They also have Cristiano Ronaldo and Jose Mourinho on their list of clients.
The Spanish stopper is out of contract at the end of next summer so United will be desperate to tie him down before the start of next season and avoid any potential risk of losing him for free next year.
He did exercise the one-year extension earlier this season to fend off interest from Europe in January, with Juventus and Paris Saint-Germain both thought to be interested.
If De Gea does sign the new deal, though, he is expected to become the club's second-highest earner.
Alexis Sanchez leads the way with a staggering £505,000 per week while Paul Pogba's improved deal last year means he is now on £290,000 each week.
De Gea joined from Atletico Madrid in 2011, winning the Premier League in his second season and has also won the Europa League, FA Cup and League Cup during his eight years at Old Trafford.
He almost joined Real Madrid in 2015 but a deadline day deal fell through and he subsequently signed a new four-year deal with United.
Manchester United have already agreed new contracts with Chris Smalling, Phil Jones, Luke Shaw, Ashley Young, Scott McTominay and Anthony Martial this season and will be desperate De Gea is next to commit his future.
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