City struck personal terms with the Italy goalkeeper earlier this month after it became clear Donnarumma was leaving Paris this summer.
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RMC says after initially demanding €50m from City to sell Donnarumma, PSG have relented are now willing to accept €30-35m to part with the Champions League winner.
A deal is now closer to being struck, which will also see Ederson sold by City to Galatasaray.
Donnarumma will join City as their outright No1, with James Trafford, re-signed from Burnley over the summer, to act as his backup.