The Arsenal manager also said the club had received an increased offer from Inter Milan for out-of-favour Germany striker Lukas Podolski.
The Southampton supporter was held by Hampshire Police after having confronted Wenger in his dugout during the Premier League game.
"The man, arrested on suspicion of going on to an area adjacent to the playing area contrary to the Football (Offences) Act 1991, remains in police custody," the police said in a statement.
Wenger said of the fan: "I don't think he said anything. It was not aggressive at all".
The Frenchman then went on to describe Inter's bid to buy Podolski in this month's transfer window.
"The first proposal was farcical," said Wenger. "After, when they come back a bit more seriously, then you will see what happens now."
Asked whether it was inevitable that Podolski would move to Inter, Wenger replied: "Inevitable? In the transfer window that's very difficult to say but we'll see what happens".
Southampton's victory lifted them to fourth spot in the table, two places above Arsenal.
(Writing by Tony Jimenez; Editing by Mark Lamport-Stokes)
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