The 21-year-old is regarded as one of La Liga’s best young defenders and City have moved for him after difficulties closing a deal for Kalidou Koulibaly.
Txiki Begiristain, City’s sporting director, has been in talks with his Sevilla counterpart Monchi since last week.
And the transfer is about to be closed for a fee of around €50m, it is reported.
The two clubs are currently negotiating how much will be paid up front and in bonuses.
Kounde has a release clause of €80m, but City were never going to pay that much.
France under-21 international Kounde was on City’s shortlist along with Koulibaly and Atletico Madrid’s Jose Gimenez.
City held talks with Atletico about a deal for Gimenez, 25, but the Madrid club referred them to his €105m release clause.
Should the deal be confirmed, Kounde will be Pep Guardiola’s second defensive signing of the summer.
Kounde joined Sevilla from Bordeaux for €25m last year and was one of the revelations of the 2019-20 season.