Berge, a 19-year old defensive midfielder, plays for Genk in the Jupiler Pro League in Belgium, having joined from Vålerenga in his native Norway in January.
The Mirror reported last summer that Everton had a £2million late offer for the then Vålerenga player turned down, and would now be expected to pay £18million to bring him to England.
However, Arsenal look to be favourites to bring in the 6ft 3in powerhouse, with Arsene Wenger looking to strengthen his midfield after a disappointing season.
With the signings of Morgan Schneiderlin and Davy Klaassen in the past six months, Everton are not short of central midfielders, with five other senior players who can occupy that position currently at the club.
Should Everton move for Berge, it is expected than James McCarthy and/or Muhamed Bešic could be set to leave Goodison Park, however it seems that Arsenal are the stronger favourites and will surely be more desperate to improve their midfield stock than the Toffees.
Sevilla and Monaco, both of whom tried to secure the player’s signature last season, could also come back in for him.