Sources say any “big” offers will be considered for the 24-year-old despite him only signing a new four-year deal until 2027 last July.
Football Insider previously revealed Arsenal could accept a £25million offer for Nelson after Brighton have shown an interest in securing his signature.
A sale would go down as pure profit in the London giants’ financial accounts because the English winger is an academy graduate.
Arsenal don’t want to damage their homegrown quota, but Nelson is considered a fringe player and a permanent move remains a possibility.
Nelson has spent the past 15 years at Arsenal after joining the club as a nine-year-old before progressing through the ranks and into the first team.
After taking in loan spells abroad with TSG Hoffenheim and Feyenoord, the winger has seen his opportunities relatively limited at the Emirates, having made just 89 appearances since making his debut in 2017.
The former England youth international started just once in the Premier League last season as he failed to register any goal contributions in his 15 league appearances.
Arsenal are willing to offload Nelson this summer if they receive a reasonable offer for his services after some of their fellow Premier League clubs have previously shown an interest in signing him.
Any funds generated are likely to go towards bringing in a new forward as Mikel Arteta is believed to be keen on strengthening his attacking options before the start of next season.
Football Insider revealed last month Arsenal have added Newcastle United star Alexander Isak to a four-man striker shortlist as they look to bring in some extra firepower.