Senegal international Ba has been attracting interest from a host of clubs with his form on Tyneside and a reported £7 million release clause in his contract, and the north London club had seemed to be at the front of the queue.
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However, Arsenal boss Wenger has ended the speculation involving a possible bid for Ba by insisting that he is not looking to sign the striker.
"It is not right to speak about [Ba] because he plays against us [on Saturday]," Wenger told reporters. "If you ask 'do we [want to] sign him?' I say no."
The 63-year-old was also asked about the possibility of signing Villa, who is out of favour at Camp Nou, but refused to be drawn on whether or not the club were interested in the former Valencia forward, insisting that all the Gunners' transfer targets will remain a "secret".
However, Wenger did not rule out a possible third spell at the club for Thierry Henry, who Goal.com revealed has already agreed to join the club in principle.
He added: "I have not lost interest in him [Henry], he is still coming today to practise with us. I have not ruled out a move completely."