It has been claimed that Fulham and Crystal Palace have both failed with approaches for the England international, who is expected to leave in search of regular first-team football elsewhere.
The Cottagers' bid was thought to be in the region of £30m, but they may be prepared to up their offer to £40m, which would make Smith Rowe Arsenal's most expensive departure of all time.
The Gunners are keen for such a scenario to come to fruition, as they have not made a higher sale since shipping Alex Oxlade-Chamberlain out to Liverpool in the summer of 2017.
Now, the Evening Standard claims that Arsenal are 'braced' to receive more bids for their Hale End graduate, but contrary to previous reports, the outlet says that only Fulham have made an official approach so far.
Arsenal 'open' to Smith Rowe departure
Nevertheless, Palace - who have lost Michael Olise this summer and are also at risk of seeing Eberechi Eze depart - are keen admirers of Smith Rowe and are weighing up an official approach of their own.
The Englishman - who became an Under-21 European champion with his nation last year - is now back at Arsenal's London Colney base for pre-season training, but the Gunners will let him leave for the right price.
Smith Rowe has long been a fan favourite at the Emirates ever since his initial breakthrough under Unai Emery, which preceded loans to German outfit RB Leipzig and Huddersfield Town.
The 23-year-old subsequently became a key player for Mikel Arteta in the second half of the 2020-21 season, after which Aston Villa tried and failed with two offers as Arsenal tied him down to a new long-term contract.
The 2021-22 season proved to be Smith Rowe's finest campaign yet, as he came up with 10 Premier League goals as Arsenal finished fifth in the table, but injury cruelly struck at the start of the 2022-23 campaign.
The midfielder has not reached the same heights since that groin operation, only managing 475 minutes of football across all competitions last season, setting up two goals in 19 appearances.
Smith Rowe to lead Arsenal academy exodus?
Smith Rowe is one of a handful of home-grown players to have only made fleeting impressions in the 2023-24 season, and he could be one of four to head elsewhere for the new campaign.
Goalkeeper Aaron Ramsdale is itching for regular first-team football after being cut to second choice last season, and his playing situation will seemingly not improve now that David Raya has signed from Brentford on a permanent deal.
Winger Reiss Nelson was also frozen out for large periods last term, while Eddie Nketiah is now Arteta's third-choice centre-forward behind Kai Havertz and Gabriel Jesus and is thought to be a prime target for Marseille.
The Gunners' summer clearout began with the exits of Arthur Okonkwo, Cedric Soares and Mohamed Elneny as free agents, while Nuno Tavares and Albert Sambi Lokonga have been loaned to Lazio and Sevilla respectively.