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 ÂŁ12 million, has scored one goal in nine league matches for Monchengladbach so far this season.
By Ollie Carroll
Twitter: @Ollie_Carroll_