Spanish outlet Cadena SER suggest Real Madrid are willing to pay £63million to bring De Gea back to Spain ahead of the 2018-19 campaign.
The 27-year-old has been linked with a move back to the Spanish capital during the past few seasons after his transfer to Real Madrid broke down in August 2015.
De Gea looked set to leave Old Trafford over two years ago but the clubs failed to submit the required paperwork before FIFA’s strict transfer deadline.
Current Real Madrid No 1 Keylor Navas was scheduled to move in the opposite direction until the deal broke down at the 11th hour.
De Gea’s contract is due to expire in June 2019 but the Red Devils have the option to extend his deal by a further year.
Jose Mourinho may choose to cash in on the highly-rated stopper in order to strengthen other areas of his team.
The Portuguese tactician has a long-standing interest in winger Gareth Bale and is keen on working with centre-back Raphael Varane again.
De Gea has been in exceptional form once again this season – keeping eight clean sheets in 12 Premier League games this season.
United have not mathematically guaranteed their place in the last 16 but they are six points clear of Basle and CSKA Moscow, who are second and third respectively, with just two games left to play.