Pep Guardiola and director of football Txiki Begiristain will push ahead with plans to sign a centre-back after missing out on a replacement for Vincent Kompany last summer.
Aymeric Laporte's injury problems this season, and doubts over Nicolas Otamendi's future, have heightened City's need to strengthen the centre of defence and the position remains the focus ahead of the new campaign. Villarreal defender Pau Torres, 23, is one of the names in the frame.
Sources have told ESPN that Leicester City's Chilwell is at the top of Chelsea's wishlist. Guardiola and City's recruitment team have also been impressed with the defender and will closely watch Chelsea's interest.
City's defence has been a problem for Guardiola this season. After lifting the Premier League title last year having conceded just 23 goals, City have leaked 31 in 28 games this term.
Following Kompany's decision to leave the Etihad after taking up a player-manager role at Anderlecht, City missed out on signing Harry Maguire.