The Gunners have been linked with the German midfielder for the majority of the summer with Arsène Wenger looking to bolster his midfield with a bit of muscle.
Khedira, currently at Real Madrid, has only one-year remaining on his contract and could find first team opportunities hard to come by in the Spanish capital this season.
Competition for places has really tightened up at the Champions League winners after they signed Colombian sensation James Rodriguez and astute passer Toni Kroos following the World Cup.
Los Blancos manager Carlo Ancelotti has expressed his desire to keep the 27-year-old in Spain, but with only a year remaining on his contract the club may have to sell now to avoid losing him for nothing next summer.
Opinionated pundit and ex-professional footballer Robbie Savage has had his say on Arsenal's transfer dealings this summer and the former Leicester City man feels Wenger has signed well in Alexis Sanchez, but needs a Khedira like player to be serious competitors this season.
He wrote in his latest Daily Mirror column: “They are going to be real contenders this time.
“Sanchez is a fantastic signing and if Arsène Wenger can add one more destructive midfielder – Real Madrid’s Sami Khedira would be ideal – they will not just be scrambling into the top four, they should be fighting for the title with Chelsea and Manchester City.”
Someone of Khedira's ability is far too good to be playing second fiddle to the likes of Kroos, Rodriguez and Luka Modric. His situation in Madrid has not only attracted the attention of Arsenal, but London rivals Chelsea and Bundesliga winners Bayern Munch are also said to hold an interest in the box-to-box midfielder.
Khedira had to recover from a serious knee injury to be fit for the World Cup, but considering his length of absence, the ex-Stuttgart man put on some impressive displays in Germany's eventual tournament triumph.