The Blues are one of several sides interested in the Wales star.
The forward is available on a free transfer this summer after leaving Championship side Reading at the end of last season.
There is widespread interest in his services though after he shone for Wales at Euro 2016.
He was recently the star man in the win over Belgium, scoring a stunning solo goal as they secured a 3-1 win to reach the semi-final stage of the tournament.
And his form in France has reportedly caught the eye of new Everton manager Ronald Koeman who, according to the Daily Mail, is now considering a move for the Welshman.
The Dutchman is set for a busy summer at Goodison Park as he looks to make use of the big transfer funds reportedly offered by majority shareholder Farhad Moshiri.
Adding to his attacking recruits is one of his aims, with Arouna Kone and Oumar Niasse having failed to provide sufficient back up to Romelu Lukaku thus far.
That has led Everton to identify Robson-Kanu as an option, with the Blues thought to be the most high profile of those currently interested in his services.