The Gunners have also been linked with West Ham striker Carlton Cole and Wolfsburg ace Edin Dzeko but The Mirror says Gignac is now Wenger’s top target for the January transfer window.
Wenger is keen on bringing in a new striker due to fitness fears for Danish striker Nicklas Bendtner, who could be out for another two months.
Wenger said: “It depends on Bendtner. How bad it is. If he is out for two months, there is no way – we will need someone absolutely.
“There is still a 50-50 chance that we sign somebody. But it’s my responsibility to spend the money in the right way, why should I splash it out and pay £10million or a player who is worth five?”