The Gunners will be left desperately short of central defenders if Sol Campbell, William Gallas and Mikael Silvestre fail to renew their contracts when they expire at the end of the month.
The Frenchman said at the end of last season that Arsenal's "average" performances at the back cost them dearly in their pursuit of a first Premier League title in six years.
He is keen to find a centre half to partner Thomas Vermaelen at the heart of the Arsenal defence for next season and has been splitting his time in South Africa between scouting and commentating for French television.
"We are not close (to signing anyone) at the moment," Wenger told www.arsenal.com.
"We are quiet. But there will be something happening before the end of the World Cup - certainly on the defensive side."