Berget has held talks with the Premier League club and is on the verge of joining countrymen Magnus Wolff Eikrem and Mats Moller Daehli at the Cardiff City Stadium.
The 23-year-old, who can also play in attack, played under Solskjaer at Molde and has opted not to sign a new deal with the Norwegian club.
Cardiff manager Solskjaer confirmed holding discussions with Berget, but said on Friday: "No other additions have been concluded."
He has been capped by Norway four times and now looks set to join Cardiff’s battle to stay in the top flight.
Solskjaer's side travel to Championship side Bolton Wanderers in the fourth round of the FA Cup on Saturday and the former Norway striker sees the tie as an excellent opportunity to secure a morale-boosting win.
"We're changing things gradually here. It will take time, but tomorrow will be an important game," he added.
"An FA Cup run would be vital for us to build momentum and a good feeling around the camp.
"We've got to build a belief that we fully belong in the Premier League and can compete at grounds like the Etihad (Stadium) and Old Trafford."
