City had a bid accepted for the 29-year-old Chilean on deadline day in August but the move collapsed.
Blues manager Pep Guardiola has discussed transfer targets for the next 18 months with the club’s hierarchy.
There are fears signing Sanchez in January could disturb the balance of Guardiola’s table-topping squad.
It is understood City think Arsenal believe keeping the former Barcelona player was a mistake and would be willing to do business next month.
However, with Guardiola’s side 11 points clear at the top of the Premier League, there is a feeling bringing in Sanchez then may cause disruption.
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