Eikrem, 23, currently plays for Eredivisie side Heerenveen, having joined them in 2013 from the Norwegian team Solskjaer managed, Molde.
His presence at Cardiff's away win at Newcastle has fuelled speculation that he will become his old boss's first recruit in the Premier League.
When asked by Voetbal International why he was watching the Cardiff City match, Eikrem was tight lipped, stating only, “I’m here for a football game.”
But the likelihood of the switch increased on Sunday when Heerenveen manager and Dutch legend Marco van Basten confirmed that Eikrem would be leaving the club so shortly after his arrival:
Heerenveen have the 23-year-old under contract for the next two years, and will expect a nice fee if they are to consider selling the midfielder this month.
In addition to his Molde ties with Solskjaer, Eikrem also spent time at the Manchester United academy having initially started off in the Molde youth ranks, and he returned to the Norweigian club in 2011 after failing to make a single league appearance for the Red Devils.
Eikrem plays primarily as an attacking midfielder, but is able to slot in anywhere across the midfield and in any position supporting the attack.
He has 13 senior caps for Norway.