Kramer is currently in his second season of the two-year loan deal he is under at Borussia Monchengladbach from his actual club Bayer Leverkusen.
And according to Goal, Arsenal are keen on the 23-year-old and have been sending scouts to Germany to watch him on a regular basis since the start of last season.
It is also understood that the Gunners are desperate to recruit a total midfielder during the upcoming January transfer window, and have been extremely impressed with Kramer’s vast development over the past year.
Kramer, who has been valued at £12 million, has scored one goal in nine league matches for Monchengladbach so far this season.
By Ollie Carroll
Twitter: @Ollie_Carroll_