The Gunners boss still wants to bring in another player to fill the void left by Thierry Henry's departure to Barcelona, and the Daily Express claims that Bolton striker Anelka is his first choice.
Wenger wanted to sign Anelka immediately after Henry's departure to Spain was confirmed, but this was met with heavy opposition from the Arsenal board, who were reluctant to sign a player with such a reputation for causing unrest.
Anelka was first signed by Wenger from PSG for £500,000, but after two seasons at Highbury he virtually went on strike after demanding first a pay rise, then a move to Real Madrid.
He eventually did make the move to Spain for £22.3million in 1999, and has since not managed to stay at a club for very long.
Despite the Gunners' board's initial reluctance, Wenger is keen to re-sign the forward, who would cost around £10million.
The Express also reports that Anelka has an offer on the table from Valencia, and the lure of Champions League football is likely to be too strong to resist.
Wenger claims that his summer transfer plans have been completely changed by Henry's departure, who he expected to stay in London.
The Gunners boss said: "I said I would not buy unless I found a super player - but at that time Thierry was staying. Then the Thierry situation was raised.
"I could not go into the new season without a striker. When he was staying I was buying one super player. The problem became different when Thierry left. Then I had to buy a striker."