De Gea has been heavily linked with a move to Real Madrid in recent months, however, the two clubs have yet to agree to a deal.
According to Spanish publication Marca, Navas could play a key role in the long-running transfer saga to allow De Gea to finally make the move to the Bernabeu.
United will be keen for a player-plus-cash deal for De Gea, and it is understood the Red Devils were keen on signing Navas following last year’s World Cup.
It could result in a win-win for both clubs and would finally see the end of the summer’s longest transfer saga’s.
De Gea was left out of both of United’s opening Premier League matches, with new signing Sergio Romero featuring in between the sticks in wins over Tottenham and Aston Villa.