The England international is Mikel Arteta's third choice number nine behind Kai Havertz and Gabriel Jesus and is expected to leave in search of regular game time this month.
Prospective moves to Marseille and Bournemouth both collapsed for Nketiah, though, as the two outfits instead swooped for Elye Wahi and Evanilson respectively.
The striker's exit from the Emirates has therefore been plunged into doubt, but according to Football Insider, Everton are set to make a loan approach within the next couple of weeks.
The Toffees' move for Nketiah will hinge on the future of Dominic Calvert-Lewin, though, and Sean Dyche's side face intense competition from Nottingham Forest, Wolverhampton Wanderers and Crystal Palace.
Nketiah has 38 goals to show from 168 games in an Arsenal shirt, but he was an unused substitute in the Gunners' 2-0 win over Wolves in Saturday's Premier League opener.
Chelsea 'agree' 21-year-old exit to Championship club
Speaking of academy products potentially leaving London-based clubs, Chelsea have reportedly struck an agreement to offload 21-year-old defender Bashir Humphreys.
The England Under-21 international has played just twice competitively for the Blues' first team since coming through their academy, making his debut in a 2022-23 FA Cup loss to Manchester City.
Humphreys's second and most recent Chelsea appearance came in last season's EFL Cup second-round thrashing of AFC Wimbledon, before he enjoyed a productive loan spell at Swansea City.
The defender was not involved in Chelsea's pre-season tour of the USA, though, and football.london claims that the Blues have now agreed to loan him out to Burnley with an obligation to buy in 2025.
Once his loan deal runs its course, Humphreys will supposedly sign a five-year contract with Scott Parker's side until 2030, having been earmarked as a standout defensive option by the Clarets boss.
Humphreys started 22 Championship games for Swansea in the second half of last season, predominantly as a centre-back, although he can also play as a right-back.
Dele Alli handed Everton lifeline after contract expiry
A player whose future is less clear, Dele Alli has been handed a lifeline by Everton, who will give him the chance to prove himself in special behind-closed-door contests.
The former Tottenham Hotspur phenom officially became a free agent when his Toffees deal ran out at the end of June, and his next career move has been clouded in uncertainty for several months.
Alli endured injury hell while representing Everton, whom he did not make a single appearance for during the 2023-24 campaign on account of a serious groin injury, which he needed surgery for.
Nevertheless, Dyche has confirmed that the Toffees have extended an olive branch to the 28-year-old and will observe his displays in behind-closed-door matches before making a decision on a new contract.
"It's not just a case of getting fit and running around with the first-team group, then he needs games, so therefore a games programme has got to come next," the Everton boss told the media.
Alli is reportedly hoping to continue his career at Everton, whom he has only made 13 competitive appearances for, and his last game in any setting came on loan with Besiktas in February 2023.
Rangers 'fall behind' in race for 21-year-old midfielder
Further north, Rangers have apparently lost ground in the race to sign 21-year-old Bayer Leverkusen midfielder Gustavo Puerta, who is close to joining Hull City.
The 21-year-old was only a bit-part player for the reigning Bundesliga champions last season, making seven appearances in the German top flight and another three in the Europa League.
Puerta also failed to make the matchday squad for Saturday's German Super Cup success over Stuttgart, and he finds himself behind Granit Xhaka, Exequiel Palacios, Robert Andrich and new signing Aleix Garcia in the pecking order.
Rangers are believed to be one of several clubs weighing up an offer, but according to Football Insider, Hull are currently leading the multi-team chase to sign the Colombian lynchpin.
Hull are understood to be close to striking a loan deal with an obligation for a permanent move in 2025, also beating Brondby, Red Star Belgrade, PAOK and Anderlecht to his signature.
The Tigers are apparently offering a sizeable loan fee to sign Puerta, who joined Leverkusen from Nuremberg for just £1.7m in January 2023.