Pogba will be available on a free transfer at the end of the season, and although Paris Saint-Germain and Juventus are leading the chase for his signature, sources close to City are not ruling out making an offer themselves.
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With club captain Fernandinho set to leave the Etihad Stadium in June, City are exploring what options are available to bolster their midfield.
Pep Guardiola is a big admirer of De Jong and was keen to sign the Dutchman when he left Ajax for Camp Nou in 2019.
Meanwhile, sources have told ESPN that Pogba would be open to joining City, who believe the World Cup winner is a viable option because of his contract situation at Old Trafford.
Pogba would likely become one of the highest-paid players at the Etihad and there would be significant fees given to his representatives, but the overall cost of the deal would be made more manageable without a sizeable transfer fee added on top.
City's top priority this summer is to get a deal for striker Erling Haaland over the line.
They have until June to trigger the €75m release clause in the Norwegian's contract at Borussia Dortmund, but sources have told ESPN that talks up to this point have been productive and that there is confidence on all sides that the 21-year-old will be a City player next season.