Paulinho is rated the next big thing to emerge from Brazil, where some rate him ahead of Real Madrid signing Vinicius Junior.
The 17 year-old has attracted a £12m bid from Atletico Madrid - which was immediately rejected. Vasco rate Paulinho in the £25m class.
City are in contact with Paulinho's minders and preparing to deliver a rival offer.
The striker's agent Carlos Leite was recently in England to meet interested clubs.