The Germany international – who recovered from serious injury problems in time to make it into his nation’s squad for the World Cup – has been a long-term target for the Gunners.
Although Barcelona’s Alexis Sanchez – a bid is said to have been made for the Chilean – is seen as Wenger’s top target, the Frenchman also wants an all-round midfielder in his ranks as he looks to build a squad capable of sustaining a title push next season.
Mikel Arteta is now seen as a little too old to be an ever-present, but Khedira on the other hand at 27 is firmly in the peak years of his career.
Real have plenty of options in the role at the Bernabeu, and with Colombian duo Radamel Falcao and James Rodriguez being mooted as targets, funds may be needed.
Khedira himself could be tempted by the chance to join Arsenal, while Manchester United have also been linked with his signature in the past.