Having impressed in the Champions League this season, Berge has been linked with a number of Premier League clubs, including top-flight leaders Liverpool.
However, according to HLN, Bramall Lane appears to be his most likely destination, providing that the Blades can strike a deal with Genk.
The report suggests that the Yorkshire side are willing to spend £17m in order to secure the services of the Norway international.
Despite the 21-year-old being open to the move, it has been claimed elsewhere that Genk may look to keep hold of the player until the end of the season.
Berge has just under 18 months remaining on his contract. body check tags ::