With the Hale End graduate seeking regular minutes at this stage of his career, Arsenal will not stand in his way of an exit for the right price, but they are yet to strike a deal with any interested party.
As many as three clubs have pulled out of negotiations to sign Nketiah, with Marseille having several bids knocked back before bringing Elye Wahi to the Orange Velodrome from Lens instead.
Bournemouth also could not come to an agreement with Arsenal and subsequently struck a deal to sign Evanilson from Porto, but a £30m move to Forest appeared to be on the cards, with Nketiah also said to have agreed personal terms with the Tricky Trees.
However, recent reports have claimed that a deal could not be reached between player and club, leaving Nketiah at risk of another unproductive season as Arsenal's third-choice striker behind Gabriel Jesus and Kai Havertz.
Palace 'rivalling European club' for Nketiah
An exit could still materialise in the closing stages of the window, though, as The Athletic claims that Crystal Palace - who have long held an interest in Nketiah - are now considering an approach.
The Eagles reportedly touched base with Arsenal to discuss Nketiah's situation earlier this summer, and the England international would be open to the switch so long as he was guaranteed regular first-team football.
An unnamed European team is believed to be rivalling Palace for the signature of Nketiah, who has three years left to run on his Arsenal deal, having last signed a long-term extension in 2022.
The 25-year-old has contributed 38 goals and seven assists in 168 matches for the Gunners in that time, winning one FA Cup and two Community Shields and briefly breaking into Gareth Southgate's England squad.
After failing to find common ground with Nketiah, Forest have apparently turned their attention back to Feyenoord's Santiago Gimenez, who was also linked with a move to Arsenal earlier this year.
Could Jesus injury change Nketiah transfer plans?
So far this season, Nketiah has only been an unused substitute in Arsenal's opening Premier League wins over Wolverhampton Wanderers and Aston Villa, with Havertz leading the line on both occasions.
Nketiah was the only recognised centre-forward on the bench for the latter game, though, as Jesus was missing from the squad with a groin injury, the severity of which has not yet been determined.
Jesus will be sent for scans on Monday, but the early indications are that he has not sustained a serious problem, and he should be back in action by the end of the September international break at the latest.
Regardless, Arteta affirmed after the win over Villa that Nketiah wanted to stay with Arsenal, and the Gunners boss is supposedly happy to keep him around, believing that he is a good depth option in attack.
However, Jesus's injury will not threaten a possible exit for Nketiah, who is still expected to head for the Emirates exit door before Friday's deadline.