Berge was at the club’s training ground on Thursday ahead of a move to Bramall Lane, with the fee set to eclipse the £20m the Blades paid for Oli McBurnie in the summer.
The 21-year-old is regarded as one of the top young midfield talents in Europe and signing him would represent a coup for Blades boss Chris Wilder, who has tracked the player for some time.
Wilder would not be drawn on Berge specifically but ahead of Friday night’s transfer deadline he said: “We are working away on a number of deals, a number of deal that we are close to getting over the line, and they will be presented in the time when everything is done out of respect to the clubs that we are working with and the individual players.
“So until they get done on the dotted line and everything is agreed, then we are still working away. I said all along I wanted to strengthen and some are close, they obviously have to be close to be completed before tomorrow night. But it is not always straightforward and a lot of work goes into it, as you can imagine.
“We wanted to strengthen while we were going well. It is important you strengthen while you are going well and we want to push on and add to the group. We are looking to get three over the line, and we are confident we can do that.
“We are working away. It is tough and of course I wouldn’t expect it to be any different and I shouldn’t be surprised that I’m getting up at the crack of dawn and going to bed in the early hours, because that is the work you have to do to make things happen and improve the club.”
Wilder, who has also been linked with moves for striker Richairo Zivkovic from Changchun Yatai and defender Panagiotis Retsos from Bayer Leverkusen, added: “Hopefully by the end of the window we will have a group that will be as strong as it has for a long long time in this club’s history and we look forward to the challenges ahead.”
Away from the transfer window, the Blades resume Premier League action away at Crystal Palace on Saturday.
“It will be a tough game,” said Wilder. “It’s a tough trip against a team in and around us but one we feel, as we always do, that we can attack and try and get a result from.
“We will have to do a lot of things right, they’ve got lot of talented players and a manager I have a huge amount of respect for.”
David McGoldrick (foot) will be assessed ahead of the trip to Selhurst Park after the striker suffered a setback in training this week.