The Premier League side, who currently sit third in the English top-flight standings, but 11 points adrift of surprise league leaders Leicester City with one game in hand, are thought to be pondering a move for the Real Madrid midfielder once the 2015-16 campaign has concluded.
The 26-year-old, who has 64 international caps for the reigning FIFA World Cup holders and featured for Germany in their 2-1 defeat to England last Saturday, has scored one goal and provided nine assists in 33 appearances in all competitions for the La Liga giants so far this season.
Kroos, who is also a reported transfer target of Premier League rivals Manchester United, is thought to have been the subject of three enquiries from the Gunners already this term over his future availability.
With the Gunners set to lose Mikel Arteta, Tomis Rosicky and Mathieu Flamini this summer, boss Arsene Wenger is keen on luring Xhaka to the Emirates Stadium.
The report suggests that United will make a renewed bid worth £40m for Kroos this summer.