The Premier League leaders - who beat Newcastle United on Saturday to remain top of the Premier League - are rumoured to be interested in signing the Egypt international following the injuries to Santi Cazorla and Francis Coquelin.
One of Elneny's former coaches claimed on Friday that he was set to undergo a medical in London but Wenger insists Arsenal are not on the verge of completing any deals.
When asked if he could provide an update on the situation, Wenger replied: "No. I have nothing to say because he's not our player and we have not signed anybody and we are not imminently in a position where we can say we signed anybody.
"We're out there to get somebody but at the moment we haven't signed anybody."
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