The 24-year-old arrived at the Cardiff City Stadium from Heerenveen last winter, but since then he has made just one league start for the club.
With his place in Norway's senior side also under threat, the midfielder has admitted that he may need to depart Russell Slade's side for the good of his career.
"For as long as I am not playing for the club, neither will I get to play for the national team. You are never satisfied when you don't play. I have hardly played for a whole year, which is not good," he told Norwegian newspaper VG.
"The only thing I can do is to play well when I get the chance. I have not spoken to the new manager and will see how things go. I now need to start playing football regularly again. It cannot continue like this."
Eikrem has made three appearances in the Championship as a substitute this term.