Yet, the France boss says that the Costa Rica international remains fully focused on giving his best for Los Blancos ahead of the first leg of the Champions League semi-finals with Atletico Madrid on Tuesday night (2 May).
Real Madrid were on the verge of singing De Gea in the summer of 2015 in a deal that would have seen Navas making the move in the opposite direction as a makeweight.
Both transfers eventually collapsed on deadline day but recent reports in Spain have claimed that Los Blancos will make a new attempt to sign the Manchester United keeper in the coming summer transfer window after Navas had enjoyed a shaky campaign at the Santiago Bernabeu.
Last week Marca reported in its front cover that Real Madrid have already agreed to personal terms with the Manchester United number one ahead of completing a summer move worth around €75m (£63.3m, $81.8m).
Zidane is aware of those speculations but is assured that they will not affect Navas ahead of the crucial last part of the season, with Real Madrid still fighting for the Champions League and the La Liga title.
Asked in a press conference how Navas has been affected by the latest reports linking the United keeper with a summer move to Real Madrid, Zidane said: "He's fine. He is in good spirits. There is much talk about these things (the potential arrival of De Gea) but he is focused on what he has to do, in his role and he looks good to me."
Zidane's own future at the Santiago Bernabeu has also been under some scrutiny in recent weeks amid suggestions that the could lose his job if Real Madrid fail to win either La Liga or the Champions League.
However, the France boss said that he is not concerned about those talks yet, but in getting a positive result on Tuesday night when Atletico Madrid visit the Bernabeu for the first leg of the Champions League semi-finals.
"I'm concentrating on tomorrow's game, I'm not even thinking about Saturday's game," the Real Madrid boss said. "This is the only thing that interests me. We don't know what's going to happen and it doesn't bother us."