The 18-year-old youngster, who turns 19 in January, made his debut for the Southampton first team aged just 17 last year in a FA Cup encounter against Shrewsbury.
He has also been a beneficiary of the new English Premier League laws that allow for nine substitutes on the bench, as he has featured on it in the league on several occasions.
The England under-18 international, who is also eligible for South Africa, is out of contract at the end of the season and yet to commit to a new deal.
According to British publication Talksport, Manchester City are among German side Borussia Monchengladbach and Belgian outfit Anderlecht who are watching the youngster.
Chauke joined Southampton from non-league Thatcham Town before signing his first professional contract at the club in January last year.
In reaction to the report shared on Twitter by City Chief, some Man City fans have have been expressing their thoughts and opinions.
They better sign the boy 🙏🏾 https://t.co/mwdK7lOWh1
— City Dyan (@_kdm9) November 16, 2021
Bring him to the blues !
— Elliot savage (@Elliotsavage123) November 16, 2021
No thanks https://t.co/MESZUb4PoK
— Keletso (@Keletso_Kippax) November 16, 2021
This isn’t Haaland https://t.co/tGwlrRUTTD
— owen (@owenmcc0lgan) November 16, 2021
great we will gonna sign another midfielder and not a striker😐
— KevinEks (@KevinEks2) November 16, 2021
this is normal proceedings for any top club tho? keeping tabs on top talents is necessary and a constant process. doesn’t mean looking at talent is taking away from chances or trying to sign the primary targets
— JD☯️ (@JDGrphcs) November 16, 2021