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The 19-year-old Norway international is generating much interest this summer, with Sevilla and Monaco also keen on signing him.
The defensive midfielder turned out 17 times for Belgian outfit Genk over the course of the campaign, during which he displayed an impressive ball-winning ability and a range of passing.
The Mirror report that the Gunners have watched Berge numerous times are now ready to move for the £18million rated player.
The report comes amid questions over the quality of Arsenal’s current defensive midfield options.
Arsene Wenger has Francis Coquelin, Mohamed Elneny and Granit Xhaka at his disposal but none are able to command a regular place in the side.