City and the Portuguese club have a close affiliation, and the two teams share information while City get the opportunity to scout their best youngsters.
And the 20-year-old Pereira is reportedly one of Gil Vicente's brightest talents.
The young centre-back has already received a call-up for the Cape Verde national team, and the report claims City will monitor his development closely.
They're unlikely to make a bid in January, with City boss Manuel Pellegrini set to explore other more established first-team targets in the winter window.
And City believe Pereira's progression would best be served by continuing to play first-team football with Gil Vicente, rather than reserve games in Manchester.
He's made eight appearances in the Portuguese top flight so far.
City have problems in central defence though, with new signing Martin Demichelis injured and Vincent Kompany also sidelined.
That's left Matija Nastasic and Javi Garcia as the club's first-choice pairing, with Joleon Lescott on the bench.