The Toffees had the Belgian ace on loan from Chelsea for the 2013/14 season, where he played a key role in helping them book a spot in the Europa League for next term.
But he is set to leave Merseyside in the coming months to head back to Stamford Bridge, where he may be sold on to Tottenham or one of many European clubs interested in his signature.
As a result Martinez will need to fill the void left by the burly youngster, and is keen to do so with Bony.
The 25-year-old Ivorian only switched to the Swans last year from Vitesse Arnhem, and enjoyed a decent debut campaign in which he netted 25 goals in all competitions.
His powerful approach has seen likenesses drawn with Lukaku, and the Everton chief sees him as a good alternative.
Bony himself has said that he is willing to stay at the Liberty Stadium despite their battle against relegation last season, yet he has also claimed that joining a bigger club would be an opportunity that he would struggle to turn down.