Ranieri took over the reigns at Nantes back in June but could be leaving the Ligue 1 club after just one season following an admission from the club's owner.
Kita was clear that there is no conflict between himself and the Italian boss but that the door was open if he wanted to return to his home country.
He told 'L'Equipe': "His future? Let's wait until the end of the season. Sincerely, I repeat: for Italy, he'd be able to leave, but nothing's been decided yet.
"As for what I think, I hope he stays because we've started a project, which we must continue, otherwise it'll be hassle on our part."
Kita continued: "There are a lot of people trying to stir controversy between the Coach and I, and there's no controversy to be had.
"He does his job, I do mine. We get on very well, it's quite normal that he's unhappy with our results, like I am, but neither of us have any problems with each other."
Nantes have not won a game since March 10, claiming just two league victories this year, but sit tenth in the table, five points off seventh-placed Nice.