The Gunners are poised to sign Elneny after Basel confirmed the Egyptian midfielder was close to departing the club "in the coming days".
However, the 23-year-old is likely to be Arsenal's sole piece of business in the transfer market after Wenger hinted as much following Saturday's 3-1 win over Sunderland in the FA Cup.
READ MORE | Wenger hopes to complete Elneny deal
"I believe that the next step is to get [Tomas] Rosicky back, [Danny] Welbeck back, [Alexis] Sanchez back, [Jack] Wilshere back and maybe we will get one player in [Elneny]," he told Sky Sports.
"Overall, I think we have no new injuries so I'm not worried. If we had the same number of injuries we would be a bit short."