De Jong has already been touted as a target for United, Tottenham Hotspur and Barcelona, seeing his valuation rise beyond the £50m mark.
The Mirror suggests that Man City were unsuccessful with a previous approach for the 21-year-old in the summer, but Pep Guardiola is unwilling to admit defeat and will make a fresh approach in January.
A new defensive midfielder is said to be the Catalan coach's priority, and Netherlands international De Jong is high on his list of targets.
Ajax have vowed to keep hold of the Willem II youth product for at least another year, but it is claimed that City are willing to test their resolve.
De Jong is under contract at the Johan Cruyff Arena until until 2022.