Pep Guardiola's side has faced uncharacteristic issues in midfield, with Rodri's absence exposing weaknesses in key matches. The Sky Blues see Adam Wharton, a dynamic midfielder who has impressed since joining Palace, as an ideal short-term solution to steady the ship.
However, the 20-year-old is currently sidelined with a groin injury and is not expected to return until mid-December at the earliest.
This complicates any potential move as the Etihad Stadium outfit requires an immediate impact to stabilise their performances.
Crystal Palace, meanwhile, are reluctant to part with the youngster in January, having identified him as a cornerstone of their long-term project. This stance could force City to explore alternative options as the transfer window approaches.