The Switzerland international must still finalise personal terms, but he is set to move to the City Ground for €35m - a club record for Forest.
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The Sun says Forest clinched the agreement after owner Evanglos Marinakis and global director Edu flew to Italy on the weekend for face-to-face negotiations with Bologna directors.
Napoli have also been pushing to close an agreement for Ndoye, but English sources now insist he is on his way to Forest.
Ndoye will arrive as a direct replacement for former Forest winger Anthony Elanga after his £55m sale to Newcastle.