New boss Mauricio Pochettino is after a frontman to spearhead what he hopes will be a realistic top-four challenge in the Premier League next season.
Chelsea's Lukaku, who spent last term on loan at Everton, is said to be top of his summer wish-list but the Belgium international is in high demand, with the Merseysiders, Atletico Madrid and Juventus all thought to be interested in a permanent transfer.
Spurs would be among the clubs willing to pay the reported £25million asking price but Pochettino is said to be lining up an offer for Bony instead.
The Ivory Coast international impressed last season for Swansea, netting 25 goals in all competitions, and has been linked with a move away from the Liberty Stadium in recent weeks.
It is thought he could be available for £15million, which would represent a saving compared to Lukaku, and is a proven Premier League goalscorer who would fit the profile of the type of forward Pochettino wants to sign.