The striker, who has been with the club since 2008, has been in impressive form this term, netting eight goals in 13 Ligue 1 appearances.
The Serbia international's future is in some doubt as his excellent performances have reportedly attracted interest from across Europe.
However, Kita is confident the club's latest contract offer will persuade the 26-year-old to stay.
"I've made contract offers to him for the last month and it's down to him to respond," he told L'Equipe. "It's impossible that he's already reached an agreement with another club as he would have told me about it.
"If he uses logical reasoning then he'll sign for us without hesitating. I've always protected Filip and if it wasn't for me he'd have left a long time ago.
"Filip needs to reflect well. He's the captain and star at one of the best teams in France. How would he cope with not being the star elsewhere? I know his personality well."
Nantes sit fourth in the French top flight and play host to third-placed Monaco on Sunday.
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