The Gunners had seemingly pipped Liverpool to the Turkey international's signature but an apparent late collapse in negotiations has seen Reds manager Brendan Rodgers declare his side favourites.
"At the moment, it is not alive. Can you be not alive and not dead? It is possible," Wenger told reporters of Sahin's potential arrival.
Whilst the Frenchman insisted he is happy with the balance of his squad, he also admitted he could still be tempted to move for a "special" player this summer.
"We will only take players who have something special," Wenger added. "We are still in the market in some positions, but overall we believe we have a very strong squad.
"We have a good mixture because we have experienced players in midfield like [Mikel] Arteta and [Santi] Cazorla, like [Tomas] Rosicky, and some young very promising players like [Alex] Oxlade-Chamberlain, [Aaron] Ramsey, [Francis] Coquelin, [Jack] Wilshere and one or two in between age wise like [Abou] Diaby, who is coming back. We believe we have a good mixture."The 62-year-old went on to express his hope that fleet-footed winger Theo Walcott will soon sign a new deal with the north London outfit.
"We try to sort it out, and we will try to sort it out one way or the other," he continued.
"We want to extend his contract, and to keep him at the club. His desire is also right, he wants to stay and we need to find an agreement."