The Costa Rican international is being tipped as a target for Diego Simeone, who is looking to replace Chelsea loanee Thibaut Coutois in between the posts next season.
Levante do not plan on selling Navas, despite the 27-year-old having only one year left on his contract, but he could be Madrid-bound if Los Colchoneros meet his reported €10m (£8m) buy-out clause.
"Atleti? It would be sensational," Navas is quoted as saying by El Mundo Deportivo. "I really like this team a lot."