Nelson, 26, has spent the past two seasons out on loan, first at Brentford and then at Fulham, and has returned to Arsenal this summer only to find himself outside Mikel Arteta's plans.
West Ham United have approached Arsenal to discuss his availability as they look to strengthen their squad for a promotion push from the Championship, and the London Evening Standard reports Arsenal have provided encouragement to the Hammers over a deal, with the winger entering the final year of his contract.
Arsenal would prefer an outright sale, though there have also been enquiries over a loan, and personal terms have not yet been discussed with Nelson, who is said to be weighing up whether he is willing to drop into the second tier. Benfica, now managed by Marco Silva - who took Nelson to Fulham on loan two seasons ago - have also registered interest in the winger this summer.
Martinelli's situation is less clear-cut. AS Roma have held initial talks with his representatives at Roc Nation Sports, but a departure from Arsenal is not considered a formality despite growing uncertainty over his long-term future.
The Brazilian has one year left on his contract, though Arsenal hold a one-year extension option that would allow them to protect his value rather than risk losing him for a reduced fee. Had Arsenal succeeded in their pursuit of Real Madrid's Vinicius Junior, Martinelli's exit before the transfer deadline would have been close to certain; with that move having fallen through, the club's hierarchy are now said to be reluctant to sanction any departure unless a suitable replacement can be found.
Bradley Barcola, watched by Arsenal scouts at the World Cup, remains an option but Paris St-Germain's £145m valuation is seen as excessive, and the France international is in any case believed to prefer a move to Liverpool amid stalled contract talks in Paris. Roma, who want a right-footed left winger, would also likely struggle to match Martinelli's current salary while meeting Arsenal's valuation of the 25-year-old.