The Daily Star says De Gea is planning showdown talks with Ten Hag about his United future.
De Gea fears his time at Old Trafford might be coming to an end and is keen to find out if he is still part of Ten Hag's long-term plans.
The Spanish goalkeeper will be out of contract at the end of this season and will become a free agent.
United have an option to trigger a 12-month extension in De Gea's £300,000-a-week deal but are said to be stalling, leaving the 31-year-old in limbo.
De Gea joined United from Atletico Madrid in 2011 and is currently the longest-serving star at Old Trafford, having won seven major trophies with the fallen giants.
De Gea will turn 32 in November before he heads to the World Cup with Spain - and knows it could be the perfect shop window for him to find a new club.