The Athletic say City are considering adding a new midfielder to the squad this month.
Luiz is being considered as he only moved from Aston Villa to Juve in the summer.
The Brazilian international was originally brought to Europe by City, although work permit issues hampered his progress with the Sky Blues.
Luiz has a contract with Juventus that runs until the summer of 2029.
It is suggested that City's interest will only consist of a potential loan – without any binding purchase option.