Pep Guardiola rebuilt his defence over the summer, eventually bringing in Nathan Ake from Bournemouth and Ruben Dias from Benfica.
Kounde, a France Under-21 international, admits he was flattered by interest from the Premier League title chasers, but in the end he was happy to stay where he was.
"The interest of a club like City is always a good thing, but I'm at Sevilla and I'm very calm,” Kounde told Sevilla FC TV.
“I'm lucky to be at a club that competes at a very good level. We have a fantastic group of players and people.
“That wasn't a bad option, but I always told [Sevilla director of football] Monchi that I would not force anything. If everyone wasn't happy, I knew I had a contract here, playing in the Champions League".
Kounde has missed Sevilla’s last three games, including their 0-0 group-stage draw with Chelsea in the Champions League, after testing positive for the coronavirus.
The 21-year-old admits it hasn’t been easy watching his team-mates playing without him, but he knows he is lucky not to be showing any symptoms.
"I feel good considering the circumstances. I'm at home and the time is dragging, but that's the way it is. I'm waiting for the test to come back negative. I haven't even lost my sense of smell and I'm totally asymptomatic.
"I miss both my teammates and football a lot. I am trying to take it philosophically and be patient, but it is somewhat different to the lockdown. I was alone in my house for two months, but there was no football and we were all in the same situation.
“Now it's time to watch football on the TV and follow my team-mates. There are days where you feel good and others are more difficult. But I'm very close to being back with the team and the worst is already over. I'm training at home so I return at the same level as before".