The Icelandic attacker has been earning rave reviews for his Eredivise displays, and almost guided his national side to World Cup qualification via the play-offs recently.
Interest in his signature is high, with the likes of Newcastle and West Ham having been linked with January moves.
Roberto Martinez is believed to be keen to beat his domestic rivals to the 24-year-old, and has already had scouts assessing the £2m-rated ace.
Any move for Finbogason would likely mark the end of Nikica Jelavic’s time on Merseyside.
Following his arrival from Rangers, the Croatian hit-man appeared to be one of English football’s most feared strikers, and helped the Toffees – under the guidance of David Moyes – to reach the FA Cup semi-final in 2012.
But his performances have dipped significantly since then, and he now appears to have lost any chance of a starting place due to the loan arrival of Romelu Lukaku.
Jelavic wants to represent his national side at next year’s World Cup and knows that he must be playing regularly to do so, making a move away from Goodison Park a tempting prospect.