Ndiaye is emerging as a genuine option for City, with the Senegal international expected to cost in the region of £80m and having already turned down a new contract at Goodison Park, where he has three years remaining on his current deal.
Tottenham are also keen on Ndiaye, and both clubs have looked at City forward Jack Grealish as a possible makeweight in any negotiation with Everton, whose resistance may soften given the depth already added to their midfield this summer.
Gakpo remains the more advanced pursuit, however. City and Spurs are both working on deals for the Liverpool winger with the window entering its final three days, though neither club has yet lodged a formal approach with Anfield.
The Dutchman was in Liverpool's starting XI for Saturday's home game against Nottingham Forest, and Liverpool's stance has not shifted: they want two further attacking signings of their own completed first, and any sale of Gakpo would need to command a significant fee regardless of timing.
A third front is also live at the Etihad, where City continue to push for Chelsea midfielder Enzo Fernández. Liverpool's Alexis Mac Allister has been mentioned as a fallback option in that position, but City are yet to make contact over a possible deal for the Argentine, with Fernández remaining the clear priority. Juggling all three targets - Fernández, Gakpo and Ndiaye - with only days left before deadline day leaves City's recruitment team facing a busy run-in to close out the summer.
The scale of the activity reflects a wider rebuild under Enzo Maresca since he replaced Pep Guardiola in the summer. City have already moved on Rodri, Tijjani Reijnders and Bernardo Silva, and confirmed the arrival of Morocco midfielder Ayyoub Bouaddi from Lille in a deal worth around €100m, freeing up both space in the squad and funds to pursue further additions.
Whichever of Gakpo or Ndiaye eventually arrives at the Etihad, City appear determined to add another forward option before Tuesday's cut-off, even if it means paying a premium given how little time remains to negotiate.