Germany midfielder Ozil has been a huge hit at the Emirates following his £42m but Arsenal are still determined to buy a striker to provide back-up and competition for Olivier Giroud.
Benzema has 18 months left on his contract, has endured a difficult season with the Madrid fans but has been starting more games and scoring goals in recent weeks.
France international Benzema, who has fallen behind Giroud in the national team, has always been one of Wenger's most admired transfer targets but the striker was reluctant to move in the summer.
But Ozil's arrival sent a clear message of Arsenal's intent and the Premier League leaders also maintained good relations with Real Madrid when they signed Ozil.
The issue could be whether Real Madrid would sell in January or would want to wait until the summer when they are likely to move for another of Arsenal's targets of last summer, Luis Suarez.
Arsenal have also been watching developments on Juventus striker Fernando Llorente – who was at last night's tennis at the O2 arena alongside several Arsenal players – but the Spaniard is now playing more regularly.
Llorente was keen on a move to Arsenal in January when he was not holding down a place at Juve because it is World Cup year but his situation has now improved.
Arsenal boss Wenger is acutely aware that his strikeforce needs reinforcements and that was emphasised after his team's defeat at Manchester United on Sunday.
As well as Giroud has been playing, there has only been Nicklas Bendtner in reserve with Lukas Podolski and Theo Walcott both out injured and they are seen as more natural wide men.
Arsenal's hierarchy have made it clear the funds and ambition is there to bankroll Wenger's title charge this season – and beyond.
But Arsenal know that a striker is a priority and their recruitment and scouting network is on red alert and they will move for Benzema given any encouragement.
Meanwhile, Arsenal are also stepping up contract negotiations for German defender Per Mertesacker whose form will be rewarded with a new long term deal.
That comes on top of keeper Wojciech Szczesny who has agreed but not yet signed a new four-year contract.
I think it would be a massive inclusion to the Arsenal side but i don't think it would be enough to give them a trophy, PS they are not going to win the league this season even though they are leading the pack...