The Egyptian worldwide suffered an ankle injury 35 minutes into Arsenal's 4-1 win over West Ham on Sunday after a challenge with Mark Noble.
But the Gunners still hope the 25-year-old can return this season and feature in Egypt's World Cup campaign.
Elneny has been in good form and is a key player for Egypt, who will be keen to him available for the summer's tournament.More news: Wynn Resorts looks to Japan
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Mohamed Salah, Ahmed Hegazi, Ahmed Elmohamady, Amr Gamal and former Egypt global Ahmed Mido have since sent messages of encouragement to the midfielder, with fans also following the gesture.
Sky Sports reporter Kaveh Solhekol wrote on Twitter: "Elneny ankle injury not as bad as feared".
The severity of the problem was initially played down by Arsenal's medical staff, who said Elneny had only rolled his ankle, provoking relief from Egypt fans on social media anxious about one of their team's stars. The midfielder will miss both of their semi-final ties with Atletico Madrid (the home one is Thursday), but he should be available if they were to make it to the final on May 16.
Wenger added the earliest Elneny could return is for Arsenal's final game of the Premier League season at Huddersfield on 13 May.