The Gunners are said to have made a renewed bid for German international Draxler as they seek to complete a deal before the transfer window closes.
But Wenger, speaking after Friday night's 4-0 FA Cup fourth-round victory over Coventry, denied a deal will happen.
"That is an illusion. There is nothing happening, honestly no," Wenger said. "We don't need to take players on the flanks - we have 17 players on the flanks."
Wenger responded to criticism from Jose Mourinho on Friday by stating the Chelsea boss is entitled to his opinion.
The Portuguese also highlighted what he views as the Gunners' favourable fixture list.
"Look at Christmas and you tell me who had the best fixtures," Wenger said.
"We played on Sunday against Everton, on Wednesday in Naples and on Saturday morning at Man City. So we do have not the same assessment on that front.
"What I said was not a complaint, it has nothing to do with Chelsea. It was just a suggestion of do you think it is right or wrong.
"Everybody is free in life to have his opinion about people. I never speak about people. I speak about facts and ideas. Never about people."
Wenger had previously suggested Mata's transfer was unfair as Chelsea have already played United twice this season and will not have to face Spaniard this term, unlike other title contenders.
Wenger said on Friday night: "If we have a chance it is down to our performances. Only about that. That is what we have to focus on.
"I was asked a question, I gave an honest answer. I am still naive enough to believe people are more interested in the ideas than about creating conflicts. But no, this is an illusion."
Lukas Podolski struck twice as Arsenal cruised into the fifth round of the FA Cup at the expense of Coventry, while Olivier Giroud and Santi Cazorla also scored.
"Podolski can score goals. When you have a good chance you want him to have it because he is a clinical finisher," Wenger said.
"He has an unbelievable short and quick backlift and he is very accurate in his finishing.
"He can score goals when he starts, when he comes on he is always dangerous."
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