City have already made Erling Haaland one of their main targets for the summer window and have already held extensive talks to sign the Borussia Dortmund striker.
But Pep Guardiola is also interested in strengthening his options in midfield this summer.
According to The Times, De Jong has been identified as a priority target to replace Fernandinho, who will leave City at the end of the season when his contract expires.
The report states that Barcelona would be willing to sell De Jong, due to their financial problems, and a £60m offer could be enough to snap up the Dutch international.
United are also in the running to sign de Jong, who worked under incoming manager Erik ten Hag for just under two seasons at Ajax.
Meanwhile, Xavi insists De Jong remains a “very important” player for Barcelona, despite the midfielder not being happy about the decision to be removed in the 1-0 loss to Rayo Vallecano on last month.
“He has to be a player who makes a difference and he does,” said Xavi.
‘There are not many players with his quality in the world.
He is the present and the future. He is a very important player for me.
He is capable, strong, he gets into the area. He has had some great games, but he has to be consistent. We had a face-to-face talk this week and it went well.
“Obviously being retired is frustrating for him, but I have to take care of the team.”
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