A serious pre-season injury has ruled out any prospect of a deal before Monday's deadline, but Arsenal's interest in the 20-year-old is understood to remain firmly in place, according to reports.
Kroupi was one of the standout performers in the Premier League last season, scoring 13 goals in 33 appearances for Bournemouth and drawing admiring looks from Mikel Arteta's recruitment team as they searched for further options on the left of attack. His breakthrough campaign also included goals against both Arsenal and Manchester United, and he found the net in Bournemouth's win over Manchester City that helped the Gunners to the title.
A fractured metatarsal suffered during Bournemouth's pre-season training camp in Austria has since ruled him out for around four months, however, taking any summer move off the table.
Arsenal are not alone in their admiration. Tottenham, Paris Saint-Germain and Barcelona have also been credited with interest in the Frenchman, though Bournemouth have consistently maintained he is not for sale regardless of suitors' intentions.
The Cherries' stance is unlikely to soften while Kroupi is recovering from surgery, and any January move would likely hinge on his fitness being fully restored by the turn of the year.
Arteta's side have already strengthened out wide this summer with the addition of Christos Tzolis from Club Brugge, while Morgan Rogers — another player considered for the left-wing role — was signed by Chelsea instead in a British-record deal.
Arsenal's longer-term interest in Kroupi reflects a broader search for sustained competition and depth on that side of the pitch, with the club expected to reassess the position once the winter window opens.
Kroupi's rise has been rapid since he joined Bournemouth from Ligue 2 side Lorient, initially agreeing a move as an 18-year-old before completing the transfer the following summer, and he quickly established himself as one of the division's most eye-catching young forwards last term. Bournemouth's valuation of the player, reported to be in excess of £80m, is likely to shape how serious any renewed Arsenal approach becomes early in the new year.