The midfielder is completing a move from Basel.
The midfielder’s transfer to the Emirates has been delayed, with a series of work permit and visa issues holding things up.
Club staff and lawyers have now almost completed the final paperwork though, and he has already passed a medical, with an announcement expected in the next 48 hours.
Indeed, manager Arsene Wenger has confirmed that is a distinct possibility with him telling the club's official website "We will see if he can qualify for Sunday."
Whether he is handed his debut will likely depend on how the squad recover from the frenetic and pulsating 3-3 draw with Liverpool on Wednesday night.
It is more likely that it will come next weekend, with Arsene Wenger having been boosted by the return of Mikel Arteta, while Aaron Ramsey and Alex Oxlade-Chamberlain have also impressed in central midfield in recent weeks.
Regardless though, the completion of the deal for Elneny will come as a big boost to Wenger’s side, who have had to rely on Mathieu Flamini as a defensive midfielder in the absence of Francis Coquelin.
The Frenchman has done well, but has struggled to match his compatriot’s energetic displays, something they will be hoping their new man can fix.