Martinelli, 25, is in the final year of his contract at the Emirates, although Arsenal have the option to extend it by another 12 months.
It remains to be seen if the Brazil international is keen on a move to Turkey.
Arsenal have bolstered their wide options with the addition of Christos Tzolis from Club Brugge, and were linked with a big-money move for Vinicius Junior before he signed a new contract at Real Madrid.
The suggestion is that Arsenal boss Mikel Arteta wants to refresh his attacking options, and Martinelli could follow Leandro Trossard through the exit door.
Martinelli scored just one Premier League goal last season, though he did net six times in the UEFA Champions League.
Galatasaray reportedly see him as a potential statement signing.
Another Arsenal attacker could be on the way out before the close of the transfer window, with Fabrizio Romano saying that Napoli are in talks to sign Gabriel Jesus.
The Serie A club are said to be aware of the "conditions to sign" the Brazilian, who has fallen out of favour at the Emirates.
But Napoli reportedly need to sell more players, and personal terms must be agreed before a deal can be completed.
"If Napoli want to close the deal for Gabriel Jesus, they can close it at any time," Romano said on his YouTube channel.
"Napoli are ready. Two factors are needed: the final agreement with the player on his contract, because Gabriel Jesus earns a lot, and then the departures.
"Napoli's departures are not over. It is true that [Romelu] Lukaku has left but they will have to continue with all the other names, because Napoli have to make more [money] before clearing space."
Former Chelsea defender Fikayo Tomori could be allowed to leave AC Milan after being left out of Ruben Amorim's squad for a pre-season friendly against Manchester United in Poland, according to La Gazzetta dello Sport.
The Italian outlet claims Tomori, 28, may be available for a fee of €10-15m (£8m-£13m).
The report claims the England international, who has been with Milan since 2021, "faces 20 intense days in the transfer market".
But it adds that it is "not a given that he will leave" this summer.
Amorim is said to favour other options at centre-back, potentially leaving Tomori surplus to requirements.
Milan reportedly reached an agreement with both Tottenham Hotspur and Juventus to sell the defender in January 2025, but Tomori wanted to stay where he was.
The report suggests a return to the Premier League could be on the cards for a player who is "bound" to attract offers.
Which English clubs might move for Tomori remains to be seen, while Italian giants Juve are reportedly "always interested".