Manager Pep Guardiola has said Manchester City "will try" to sign a central defender this summer.
Eliaquim Mangala is expected to depart, which would leave City with Vincent Kompany, John Stones and Nicolas Otamendi as established centre-backs.
"We don't have too much more to spend but we are going to see," said Guardiola, speaking before Saturday's friendly with Tottenham (23:00 BST).
City have spent about £200m this summer - £120m of that on three full-backs.
In the past week, Kyle Walker moved from Spurs for £45m, Danilo joined from Real Madrid for £26.5m and Benjamin Mendy was recruited from Monaco for £52m.
They join Portugal midfielder Bernardo Silva (£43m) and Brazilian goalkeeper Ederson Moraes (£35m) in arriving at City this summer.
City have also been linked with moves for Arsenal's Chilean forward Alexis Sanchez and another Monaco player, £160m-rated teenage striker Kylian Mbappe.
However, Guardiola declined to answer questions on that duo, stating that "they are Arsenal and Monaco players".