The 23-year-old is allegedly 'desperate' to leave the La Liga outfit this summer and play at a higher level amid interest from the likes of City, Chelsea and Barcelona.
Now that the Citizens have allegedly agreed to sell defender Nathan Ake to Chelsea, Pep Guardiola will look to bolster his options at the back before the September 1 deadline.
However, a potential replacement may not come cheap, as Vital Football claims that the Premier League champions will need to stump up €75m (£65m) to recruit Kounde from Sevilla.
Man City may focus their attention on signing Kounde after being dealt a blow in their pursuit of RB Leipzig's Josko Gvardiol, who is allegedly set to sign a new long-term contract with the Bundesliga side.
Kounde, who has made 133 appearances for Sevilla across all competitions over the last three years, has just two years remaining on his contract at the Ramon Sanchez-Pizjuan Stadium.