The Norwegian play-maker, who currently plays for Dutch side Heerenveen, is set to move to South Wales after United hero Solskjaer replaced Malky Mackay as Cardiff City manager.
His manager in Holland, Marco van Basten, bemoaned the 23-year-old's departure, saying; "It's a shame he's leaving because he's been important to us in the first half of the season."
Eikrem was a star for the Manchester United reserve team under Solskjaer, and followed the former striker back to Norway when the new Cardiff boss moved to Molde in 2011.
Eikrem was a key part of the Molde team that won back to back Tippeligaen titles in 2011 and 2012, before moving to Holland with Heerenveen last summer.
But after just six months with the Dutch side, the lure of working with Solskjaer again has Eikrem on the move once more, with rumours beginning yesterday after Eikrem was seen at St. James' Park for Cardiff's FA Cup tie with Newcastle United.
Cardiff will be hoping for Premier League survival, and adding a player like Eikrem, whose passing and quality from set-pieces will be key to their hopes of earning a second season in the top flight.
Eikrem already has 13 caps for his country and is tipped to become a star of the future; and a return to the Premier League should help his cause in both the short and long term.
Meanwhile, Eikrem will be joined in South Wales by another former Manchester United and Molde starlet in Mats Moller Daehli, with the Norwegian side confirming the 18-year-old has travelled to the Cardiff City Stadium ahead of his proposed move to join forces with Solskjaer once again.
image: © Jon Candy