Sahin has been strongly linked with a move to the Premier League after starting just two league games for Real Madrid last season following his arrival from Borussia Dortmund.
He was mooted as a makeweight in Real’s bid to sign Tottenham Hotspur midfielder Luka Modric, but Sahin last month stated his intention to remain at the Santiago Bernabeu.
However, Real coach Jose Mourinho confirmed earlier on Friday that it may be in the 23-year-old’s interests to take in a loan spell in order to play regularly.
“I want to be honest and Sahin is living in this grey zone because the market is open,” Mourinho told Marca.
“If the possibility arises for him to go to another place it would be better for him to leave and to be able to have more minutes on the pitch.”
But, speaking after Arsenal lost 2-0 to Manchester City in a pre-season friendly in China, Wenger denied he has added Sahin to his squad.
Wenger, who has also been linked with Santi Cazorla, commented: “We did not sign anybody today, this report is wrong. We are not signing anybody at the moment – we are not close. In the future you never know.”
Regarding the future of captain Robin van Persie, Wenger added: “We could come back forever on Van Persie. We have our main strikers at home and Van Persie is one of them. But we have Podolski and Giroud who are at home, so we have plenty of strikers.
“For us at the moment it is to prepare for the season – it is more than any individual player.”