Chelsea are not actively looking to sell the Portugal international, and the Blues have reportedly set a £70M asking price on him this summer, as they look to block City's advance on the ex-Wolves winger.
Neto joined Chelsea in a deal worth around £51M in 2024 and has gone on to win the UEFA Conference League and the FIFA Club World Cup since then.
Tottenham were previously linked with an offer, but their focus is now on City winger Savinho, who Maresca is open to selling to fund a push for Neto.
City's main rivals for Neto could now come from the Saudi Pro League with Al Hilal prepared to meet Chelsea's asking price and offer the 26-year-old an eye-watering salary.
The call over heading to the Middle East could come down to Neto himself - and it's been another summer of heavy spending in Saudi Arabia - with Francisco Trincao, Crysencio Summerville and Samu Costta making the move.