City have reportedly agreed personal terms with Kounde over a summer transfer, with the defender now being tipped to sign a five-year contract at the Etihad Stadium.
Kounde's stock has risen considerably since his €25 million ((£23m/$30m) switch to Sevilla from Bordeaux in 2019, as he helped Julen Lopetegui's side finish fourth in La Liga and win the Europa League last season.
Real Madrid and Barcelona have also been linked with the 21-year-old, who is reported to have a release clause in his current contract which is set at €75m (£69m/$88m).
Kounde played down rumours of a potential move away from Ramon Sanchez-Pizjuan Stadium last week, telling Marca: "I'm good at Sevilla. Next season we are going to play in the Champions League and we all deserve it. I am very focused and very happy here.
"It is something that I control, but sometimes there are parameters that do not depend on me. I do not look away [from Sevilla]."
Monchi has now confirmed that Sevilla have rejected an official opening bid for the centre-back, and that they are willing to consider any improved offers, but he expects a prized asset to remain focused on his duties ahead of a UEFA Super Cup clash against Bayern Munich on Thursday.
"I doubt that Kounde has an agreement with Man City because he has a contract with us. It's true, in the last days we received an offer from a club to sign Kounde, he heard about it and we rejected it," the Sevilla chief told a press conference.
"If they make another offer, we will listen to them again and we will answer but only we can choose when we will answer them.
"I know Kounde pretty well, and I'm sure he is focused on how he will defend against [Robert] Lewandowski, [Leroy] Sane, [Serge] Gnabry or [Thomas] Muller."
Asked if Sevilla will need to sell some of their more high-profile players in order to balance the books amid the coronavirus crisis, Monchi responded: "Sevilla have a model from the last 20 years (to sell players).
"We got to play in 20 finals and won 10 titles using this model and I recommend that we do not change it.
"We said no to an offer that multiplied by two and a half times the amount that we paid last year for a player who was labelled as being expensive."