That’s according to Spanish media outlet Don Balon who reckon a shock double deal could be on the cards.
De Gea is a long-term target for Real president Florentino Perez.
He was on the cusp of a move to the Bernabeu in 2015 – but the transfer collapsed due to administrative issues.
Since moving to Old Trafford from Atletico Madrid in 2011, De Gea has firmly established himself as one the Europe’s top shot stoppers.
Real are desperate to replace Keylor Navas and could be willing to spend big to finally get their man.
Pogba, meanwhile, has also been tipped to leave the Premier League after a tumultuous few months at Old Trafford.
The 24-year-old midfielder has had injury woes, slumps in performance and an increasingly strained relationship with Jose Mourinho.
The Portuguese chief wants Pogba to be utilised in a defensive capacity, but the talented playmaker prefers to be more box-to-box.
With his woes at Old Trafford intensifying, Pogba’s representative – Mino Raiola – is said to be offering him to Europe’s elite clubs.
United edged past arch-rivals Liverpool 2-1 yesterday.
Two goals from Marcus Rashford helped the Red Devils secure the win.
Pogba, however, was missing through injury and was withdrawn from the squad on Friday.
Youngster Scott McTominay was promoted from the substitutes bench to the first XI.