The Juventus full-back ruled himself out of their crucial Champions League match against Benfica. City had a £54.5 million offer rejected, with Juventus demanding £75.5 million, as per The Mirror.
A compromise is expected this week after Juve coach Thiago Motta revealed Cambiaso cited an ankle injury for his absence.
Juventus are already seeking a replacement, targeting Feyenoord's David Hancko.
Cambiaso's potential move to City is seen as a replacement for Kyle Walker. The deal highlights City's intent to strengthen their defence.