De Gea has been linked with a move to Madrid for a number of months but Man United are reportedly playing hardball with negotiations.
Louis van Gaal was said to have expressed an interest in Navas last season and he could sweeten the deal in any transfer involving De Gea.
However, United are adamant that progress with De Gea is dependant on Sergio Ramos.
The club are very interested in signing Ramos but they are aware that the possibility of a transfer will be remote if they lose De Gea.
Navas joined Madrid on the back of a superb World Cup with Costa Rica in 2014 but he has struggled to hold down a regular spot in the starting XI.
Hugo Lloris and Bernd Leno have been touted as potential replacements for De Gea but Navas may represent a cheaper and more convenient option.