The Gunners sought to add a new face to their midfield ranks over the summer and were initially expected to complete a deal for Leicester City's Youri Tielemans.
Elneny penned a new one-year deal over the summer and could therefore enter talks with foreign clubs in January, and it remains to be seen if he will be handed another extension by the Gunners.
Palmeiras and Brazil starlet Danilo has been strongly linked with a switch to the Emirates in recent months, although it has since been claimed that Arsenal are not actively pursuing the 21-year-old.
However, journalist Fabrizio Romano insists that Arteta's side remain attentive to Danilo's situation, although there are no advanced talks with Brazilian champions Palmeiras.
"There are many names on the list including Danilo of Palmeiras, a player they have followed for a long time, but at the moment, there is still nothing advanced," Romano told GiveMeSport.
Danilo represented PFC Cajazeiras before making the permanent switch to Palmeiras in the summer of 2020, and he was an integral cog in their 2022 title-winning team.
The 21-year-old ended the 2022 season with seven goals and four assists from 58 appearances in all competitions, making 34 appearances in Serie A and also playing two games at the Club World Cup.
Danilo has recorded a total of 12 goals and nine assists from 141 games for his current club, where he has also won two Copa Libertadores titles and a Recopa Sudamericana.
The former Brazil youth international only signed a new contract with Palmeiras in February of this year, and his current terms are not due to run out until the end of 2026.
While Arsenal remain keen on signing a new midfielder, the Premier League leaders' immediate priority is reinforcements in attack following Gabriel Jesus's knee injury and subsequent surgery.
Arteta's side are pushing to complete a January deal for Shakhtar Donetsk attacker Mykhaylo Mudryk, although they have already seen a bid of €65m (£57.7m) turned down.
In Jesus's absence, Eddie Nketiah led the line in Monday's showdown with West Ham United and scored the Gunners' third goal in a 3-1 come-from-behind win at the Emirates.
Arsenal remain five points clear of Manchester City at the top of the Premier League table and will close 2022 away to Brighton & Hove Albion on New Year's Eve.