The Ivory Coast international only joined the Swans last year from Vitesse Arnhem, and has enjoyed a good debut campaign in the Premier League after a shaky start.
His performances – and 10 league goals – have alerted Martinez, who is already planning for life without Romelu Lukaku.
The powerful Belgian looks unlikely to make his loan stay at Goodison Park a permanent one this summer, which will leave a huge void in the Toffees’ attacking ranks.
Bony is seen as a good like for like alternative, with the former Eredivisie star sharing some similarities in terms of playing style with the current Merseyside idol.
Swansea are unlikely to be keen to sell, but with Everton set to present the 25-year-old with a more likely chance of European qualification in the future, the player himself may be keen.
Martinez has also been linked with a string of other big names as he plans a rebuild ahead of next season, including Manchester City’s Javi Garcia.
The Spanish midfielder looks to be surplus to requirements at the Etihad Stadium, and could jump at the chance of regular playing time.