The Egypt international didn’t feature in the Champions League on Tuesday night as Arsenal suffered a 2-0 loss to Barcelona at the Emirates Stadium.
Arsenal manager Arsene Wenger signed the defensive midfielder in a £6.7m deal from Swiss champions Basel in the January transfer window.
Former Gunners striker Wright questioned why Wenger has utilised Elneny in recent weeks after their disappointing loss to Barcelona.
“I really want to start seeing Elneny more now,” Wright told BT Sport.
“He is someone who came in in January. I thought that he was signed to give a boost or make a difference at a time when Arsenal need it. He didn’t come on [against Barcelona].”
Elneny made his full Arsenal debut in the FA Cup last weekend as the defending champions were held to a goalless draw with Hull City in the fifth round at The Emirates.
The north London side make the trip to bitter rivals Manchester United in the Premier League on Sunday afternoon.
The Gunners are in third place in the Premier League table and two points behind leaders Leicester City after their 2-1 win against the Foxes.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news