The Reds are continuing to rebuild following the exit of Luis Suarez and are keen to land the Ivory Coast international this summer.
Swansea is determined to maximize any potential fee for Bony and is looking to get around 24 million euros from Liverpool, which has money to spend after agreeing to a deal to sell Luis Suarez to Barcelona for 95 million euros.
Liverpool has so far offered 16 million euros for the Ivory Coast international, but is now ready to raise it to 19 million euros, plus significant add-ons.
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Bony, who scored two goals at the World Cup in addition to his 26 club goals in 2013-14, has also attracted interest from Tottenham, and the North Londoners remain interested in acquiring the 25-year-old.
Swansea is aware of the interest from the two clubs and is open to a sale, having signed Bafetimbi Gomis from Lyon.
In addition to Gomis, the Welsh club also has forwards Marvin Emnes and Rory Donnelly on the books and has been linked with a 6 million-euro move for Watford striker Troy Deeney.
Liverpool still has money to spend and has already signed four players, with Adam Lallana, Rickie Lambert, Emre Can and Lazar Markovic all moving to Anfield in this offseason as the club seeks to rebuild following the departure of Suarez.