The Brazilian's stock has fallen since Real turned down loan and permanent enquiries alike earlier in the window, though Vinícius Júnior's decision to sign a new deal at the Bernabéu rather than join the Gunners has redirected Arsenal's search toward Endrick instead.
Endrick, 20, had struggled to establish himself during his first season and a half at Real Madrid, but a productive loan spell at Lyon in the second half of last season — eight goals in 21 appearances — put him back on the radar of Europe's biggest clubs.
Arsenal have made an official approach and are prepared to test Real Madrid's resolve, though head coach José Mourinho has made clear he does not want to lose the forward before the deadline.
"He's a player I like a lot and who has had many contacts from clubs that wanted him on loan or transferred," Mourinho said.
"I didn't want to loan or sell him because I like the player, and I'd like to work with this young player who has important talents."
Endrick has scored seven goals in 40 appearances for Real Madrid since his move from Palmeiras, a modest return for a player signed with such fanfare, but his form in France reignited interest from several clubs, with Arsenal now the most concrete suitor as the window enters its final days.
Mikel Arteta has made no secret of his desire to add another forward option before Tuesday's deadline, having already lost out on Morgan Rogers to Chelsea earlier in the window and with a separate pursuit of Atletico Madrid's Julián Álvarez dragging on amid Atlético's public refusal to sell to Barcelona.
Endrick's versatility — capable of playing centrally or from the right, as he did regularly at Lyon — would give Arteta a different profile to anything currently in his squad, even if a deal remains far from straightforward given Mourinho's stated opposition to selling him.