The 23-year-old helped Molde to reclaim the Norwegian league title last year and is being chased by Turkish giants Trabzonspor.
There is further interest in Brynhildsen though and he could have an option to move to the Premier League.
Nottingham Forest are showing interest in the attacker as part of their plans to strengthen their squad before the transfer window closes.
And Dutch giants PSV Eindhoven are also keen as they have yet to replace Cody Gakpo, who they sold to Liverpool earlier this month.
Brynhildsen scored eleven goals in 19 outings in the Norwegian top flight last season as he picked up the title.
He has now made over 100 appearances for Molde during his time at the club and is tipped to welcome a new challenge.
Brynhildsen has been capped by Norway at international level.
It remains to be seen if he can move before the transfer window slams shut.
