Forest also saw an offer said to be worth £25m plus add-ons rejected with doubts also emerging over whether Nketiah would be prepared to take a cut on his £120,000-a-week salary at the Emirates.
But the 25-year-old striker now appears set to move to the City Ground with Fabrizio Romano reporting personal terms have been settled.
Forest are also confident of agreeing a fee of £30m with Arsenal to get the deal across the line.
The development comes after Forest saw an improved offer for Feyenoord striker Santiago Gimenez rejected by the Dutch giants.
The latest bid, thought to be £22m plus £3.4m in add-ons, was not enough to sway Feyenoord into doing business, with Forest promptly turning their attention back to Nketiah.
The Londoner made his senior Arsenal debut in 2017 with a brief spell on loan at Leeds United during the 2019-20 season.
He scored six goals in 37 appearances – just 13 of those starts – last season but played a peripheral role in the club’s title challenge, not starting a league match after a 2-1 defeat to Fulham in December.
Kai Havertz and Gabriel Jesus were Mikel Arteta’s preferred options up top for much of the campaign with the German leading the line in last week’s new season opener against Wolves.
Nketiah will join fellow academy graduate Emile Smith Rowe in leaving the Emirates this summer with the attacking midfielder joining Fulham in a deal that could rise to £34m with add-ons.
Arsenal have made just one major signing this summer in Riccardo Calafiori but will hope to wrap up a deal for Real Sociedad midfielder Mikel Merino.