According to Sport, Khedira will sign a four-year deal at the Emirates after it emerged that Chelsea were also interested in the 27-year-old.
Contract talks between Khedira's representatives and Real Madrid broke down and they are now set to sell rather than let him go for free next summer.
Recruiting Khedira would be another bold statement of intent from Arsenal. After a season spent primarily on the sidelines, the German international has used the World Cup to rebuild both his reputation and his fitness.
The minor calf problem that caused him to miss the final should not detract from his contribution across the entire tournament; Khedira was arguably the star of the semi-final victory over Brazil.
However, there are those among the Arsenal fans who are concerned about the possibility of Khedira moving to north London. If the Gunners were to recruit a new midfielder this summer, many hoped it would be a purely defensive player to balance out the creative talent in the team.
With the likes of Aaron Ramsey and Jack Wilshere bombing on, it was felt that Arsenal required a player with tactical discipline to provide the team with a reliable anchor.
Khedira is not a traditional holding midfielder. In Brazil, he has occasionally been deployed as the most advanced of Germany’s midfield three, breaking into the box to seize on loose balls. His style is more akin to that of Aaron Ramsey than archetypal defensive midfielder Gilberto Silva.
It’s possible that Wenger doesn’t consider a designated holding midfielder entirely necessary. In the modern game, the inclusion of a midfielder whose sole responsibility is to protect the back four is increasingly rare.
The best midfielders are all-rounders. None of the German trio of Khedira, Bastian Schweinsteiger and Toni Kroos could be called an out-and-out defensive player, and yet they’ve won the World Cup.
Aaron Ramsey’s goals tend to grab the headlines, but he also goes through an enormous amount of defensive work. Wenger may trust Khedira and Ramsey to share defensive duties, giving him a midfield with real flexibility.
Alternatively, perhaps Wenger is considering converting Khedira to suit his needs. Lest we forget, this is the manager who made a central midfielder of former Monaco left-back Emmanuel Petit. Mikel Arteta was not a straight defensive midfielder when he arrived. At Everton, he had played in a variety of positions, including No. 10 and left-wing. Under Wenger, he underwent a steady transformation in to a sitting pivot.
Khedira has the necessary attributes to make a similar adaptation. Like Arteta, he is able to call upon intelligent positional sense, accurate passing and strong tackling. Crucially, he is more powerful than the Spaniard. If Khedira settles in a deep-lying role, he would still provide the Arsenal midfield with the fresh injection of physicality it needs.
James McNicholas is Bleacher Report's lead Arsenal correspondent and will be following the club from a London base throughout the 2013-14 season. Follow him on Twitter here.