Manager Pep Guardiola missed out on Jorginho and Fred, who joined Chelsea and United respectively, last summer.
He was also keen to sign Frenkie de Jong from Ajax but the 22-year-old Dutchman has agreed to move to Barcelona in a £67m deal at the end of the current campaign.
He needs a long-term replacement for Fernandinho, 33, and Ndombele has the required attributes to fill the Brazilian’s shoes.
As well as being a physical presence, the France international is known for his excellent passing and dribbling abilities.
Tanguy Ndombele is a reported transfer target for Manchester United and Manchester City (Image: GETTY)
Guardiola has previously said he will not be held to ransom in the transfer market after missing out on De Jong.
“The transfer market, the salaries, increase a lot," he said last month.
“After Neymar [moved to] PSG [for £200m], prices increased to incredible levels. We have to be quicker and smarter and try to buy the players.
“We have to adapt. It’s difficult to buy top, top players at a good price. It’s almost impossible.
The Lyon star is one of the most highly-rated midfielders in Europe (Image: GETTY)
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City boss Pep Guardiola needs a new midfielder but says he won;t be held to ransom in the market (Image: GETTY)
“Maybe we have to trust in the young players [in the academy] and help them develop their own personality here.”
On De Jong, he added: “I said many times – Barcelona and [Real] Madrid: it’s impossible to fight against them, for the prestige, the incredible league, the incredible clubs they are.
“The players have to take their own decisions. When they don’t want to come it’s because they want another place.
“There are other options but we are going to try if we believe we need players in that position.”