The Toffees have had the youngster on loan from Chelsea all season, but look unlikely to be able to make his stay a permanent one unless they can sneak into the final Champions League qualification spot before the season ends.
Lukaku himself is also likely to cost in excess of £20m and is wanted by a host of other top clubs, which may prevent the Merseysiders from sealing a deal.
As a result Martinez is scouring the market to replace his 13-goal hit-man, and has settled on Bony.
The Ivorian has enjoyed a fine debut season in the Premier League with the Swans after joining them from Vitesse Arnhem, despite the South Wales outfit having been off of their best.
Everton are keen to tie up a quick deal for the 25-year-old, with the club anxious that a good World Cup display could see his value rocket.
Swansea paid £12m for their man last year, but could be willing to sell if a bid of around £20m is received.
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