The Reds have been heavily linked with the Ivory Coast international in recent times, following the news of Luis Suarez’s £75m switch to Barcelona.
With the man who netted 31 Premier League goals no longer a part of the Anfield set-up, Brendan Rodgers is known to be desperate to replace him, and has set his sights on Bony.
The powerful front-man netted 26 times in his debut season at the Liberty Stadium, and is thought to be ready to move on swiftly to play in the Champions League.
Liverpool have reportedly been talking to his representatives and are understood to have lodged a £12.5m offer.
However, the Swans are keen to get around £19m for their star.
Although the Merseysiders are far from willing to go that high, they are ready to hand the South Wales outfit £15m plus potential add-ons to push through a deal.
Bony enjoyed a fine first season in English football and transferred his form to the World Cup, where he netted twice for Cote d’Ivoire, despite their poor showing.
Tottenham are also tracking the 25-year-old.