The Costa Rica goalkeeper is on the brink of joining los Blancos from fellow La Liga club Levante following his exploits at the World Cup, with Madrid having agreed to pay his £8m release clause.
And former los Ticos international keeper Conejo, who earned 29 international caps and appeared at the 1990 World Cup, believes Navas has all the right attributes to succeed in Madrid.
"There is more pressure than received in Levante as [they are] a small team," the 54-year-old told AS.
"But inside the soccer field when you have the maturity he has, that does not matter."
Navas was one of the star performers in Brazil, keeping three clean sheets - only Jasper Cillessen, Sergio Romero and Manuel Neuer managed more - as Costa Rica reached the quarter-finals for the first time in their history.
"He is the most complete goalkeeper in every sense of the modern goalkeeper," Conejo said of the 27-year-old.
"He has exquisite technique with both legs."