According to a report from Turkish outlet Ajansspor, Pep Guardiola like the 25-year-old a lot, and he is keen to bring him to the Etihad Stadium this summer, amid interest from other top European clubs.
Soyuncu is also reportedly interested in signing for City if he is granted permission to leave Leicester City.
While Leicester are not against selling Soyuncu this summer, with his contract expiring in 2023, they would demand around €50-60 million for him.
Paris Saint-Germain are one of the clubs competing with City for his signature, with them also trying to sign the defender last summer, yet Soyuncu rejected their offer.
Despite this, PSG are still interested in the Turkish international this summer, and could submit an offer soon.
La Liga giants Barcelona and Real Madrid are also interested in signing Soyuncu, with Real Madrid in particular being most eager, seeing him as the ideal replacement for Sergio Ramos, who has left the club after his contract expired at the end of June.
Barcelona are in a difficult financial situation, and so raising funds to sign the Leicester defender will be difficult to do for the Catalan outfit, especially since they are still trying to offload plenty of players.
Despite the interest across Europe, no bids from PSG, Real Madrid or Barcelona are in the process of being submitted, with only Manchester City set to make an offer for Soyuncu.
City also have the advantage of having Ilkay Gundogan in the squad, who is a close friend of Soyuncu, with there also being reports that the German wanted City to pursue the signing of Soyuncu last summer prior to signing Ruben Dias.
Soyuncu has just come off the back of a poor Euro 2020 campaign with Turkey, after his nation were eliminated in the group stages without picking up a single point.
He had a mixed season with Leicester, suffering from periods of injury and COVID-19, yet whenever he played he was a standout performer alongside Wesley Fofana, with Soyuncu making 32 appearances for Leicester in all competitions.