The Germany international has been a reported target for the Premier League club in recent months, with Arsenal thought to have been keen to further strengthen the centre of their midfield.
Rumours intensified after Real brought in Khedira's compatriot Toni Kroos from Bayern Munich, but Wenger insists Arsenal never in the market for the 27-year-old.
The Frenchman confirmed on Friday that the former Stuttgart man is unlikely to come to the Emirates Stadium, but revealed that he could yet make further signings.
Wenger questioned: "I don't know who has put Khedira on the market - is it his agent or the press?
"We were never close to signing him. Jack Wilshere is back fit and in midfield we have offensive midfielders and quite a few box-to-box players."
Arsenal have also been linked with Borussia Dortmund star Marco Reus and Sporting Lisbon midfielder William Carvalho ahead of their Premier League opener against Crystal Palce on August 16.
While remaining open to additions, Wenger said the return of Joel Campbell from a loan spell at Olympiacos and a lack of big-name departures means his squad is already very strong.
"We still have three and a half weeks before the transfer market closes," he added.
"I am open to [more transfers] but Joel Campbell has come back plus the addition of the four players we have already bought.
"We have not lost players until now so we have a big squad at the moment."
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