The 18-year-old has recently emerged as one of the top prospects in Brazilian football, despite his game time coming down in the second tier.
During Vasco da Gama's recent promotion-winning campaign, the teenager chipped in with eight goals from 33 appearances, and he has 37 outings to his name in total.
Nevertheless, despite possessing a contract at his current club until 2027, it appears increasingly likely that he will move to Europe over the coming weeks.
Last week, it was claimed that Chelsea were the clear favourites to secure the signature of Santos having been in advanced discussions over a deal.
However, according to Calciomercato, a transfer to Stamford Bridge is not necessarily a foregone conclusion at this time.
The report claims that Man City have been monitoring the situation ahead of putting forward their own proposal for Santos.
City are said to be confident that Pep Guardiola can play a pivotal role in the negotiating process as they look to secure a deal for yet another young Brazilian player.
Since 2020, City have signed the trio of Yan Couto, Diego Rosa and Kayky, although the three players in question remain some way off the City first team.
Twenty-year-old full-back Couto is currently at Girona, where he has made five starts and five substitute outings in La Liga, while midfielder Diego Rosa is at Portuguese side Vizela with three starts and six substitute appearances being accumulated.
Kayky is also in Primeira Liga with Pacos de Ferreira, where he has been restricted to three starts and five substitute outings with the forward yet to register a goal or assist.
Newcastle United have also been credited as admirers of Santos, although much may depend on how he would like to continue his development over the coming seasons.
Each of the three clubs in question are expected to be willing to meet an asking price which is said to be in the region of £12m.