Earlier this year, the Premier League champions allegedly reached an agreement with Atletico Mineiro to sign the 18-year-old on a permanent deal this summer for a fee in the region of €6.5m (£5.5m) plus add-ons.
As soon as the deal is finalised, Man City intend to loan out Savio - also known as Savinho - ahead of the 2022-23 campaign.
A report from Goal BR earlier this month claimed that the Citizens were looking to loan the teenager to Ligue 1 outfit Troyes, who are owned by City Football Group.
However, journalist Fabrizio Romano states that City are now set to send the talented Brazilian to Dutch giants PSV on a temporary deal, with both clubs in the final stages of negotiations.
Savio has featured 31 times for Atletico Mineiro's senior team, including 11 appearances across all competitions in 2022, and he has also represented the Brazil Under-16s national team on six occasions, scoring four goals in the process.
The potential arrival of Savio at PSV may cast doubts over the future of Cody Gakpo, who has been linked with a move away from the Eredivisie club amid reported interest from the likes of Arsenal, Chelsea and Liverpool.