The new Bluebirds boss has been busy in the transfer window since he arrived at the start of the month as he first brought in Norwegian duo Magnus Wolff Eikrem and Mats Moller Daehli, while a loan deal for Manchester United winger Wilfred Zaha is expected to go through.
He hopes to tie up a deal for Wigan defender Ramis and then sign 23-year-old Berget from his old club Molde.
The attacking midfielder, who can operate out wide or also as a more regular centre-forward, has said in the past that he will not renew his contract at Molde when it expires in the summer and he is keen to be reunited with Solskjaer in South Wales.
Reports in Norway say he is set for a medical at Cardiff before the weekend and is then expected to agree personal terms over the move.
"I feel ready for new challenges now," Berget had told Norwegian paper Hadeland. "My contract runs out this summer, and I'm not going to extend."
A deal for Ramis, meanwhile, is also expected to be completed after the 29-year-old held talks earlier this week.
The Spaniard has been struggling with injuries at Wigan for much of the campaign so far and has played just seven Championship matches but is now fit and keen to return to the Premier League.
It is thought Cardiff will have to pay in the region of £1.5million for the experienced defender.