The 31-year-old's current deal at the Etihad is up in June and fresh terms have so far not been forthcoming.
So Navas looks set to draw a line under four seasons in English football with a move back to Spain reportedly most likely.
However, according to reports in Italy, Roma are ready to offer him the chance to test himself in Serie A.
It has been suggested that the Italian side would be willing to hand him a three-year deal with an annual salary worth around £2.5million.
Navas made no fewer than 30 Premier League appearances in his first three seasons at City after joining from Sevilla in 2013.