Former Manchester United defender Gerard Pique is reported to have told Messi the revelation and the pair now presume that he is set for a move to Real Madrid.
That is according to Spanish outlet Diario Gol, who say De Gea’s partner Edurne, who is a Spanish singer, is helping with the search for a new property.
The couple are looking in the area of La Moraleja which is thought to be in anticipation of a summer transfer.
Real have been searching for a permanent replacement for Iker Casillas who left the club in 2015.
Keylor Navas has been holding the fort in recent years but president Florentino Perez is said to be unconvinced in the Costa Rican.
So Real are preparing to launch a bid this summer to tempt De Gea from Old Trafford.
The 27-year-old came close to moving to the Spanish capital three years ago but the deal broke down because of a faulty fax machine.
But he would be expected to complete the move this time around when the La Liga champions come knocking.
If the deal does break down, Real apparently have Chelsea’s Thibaut Courtois as their contingency plan, according to Diario Gol.
But a move for the Blues keeper would seriously hinder any chance of a deal for Eden Hazard, who is also on their wanted list.