The Ivorian forward enjoyed a fine maiden campaign in the Premier League, scoring 17 times in 34 appearances.
Recent reports have suggested that Arsenal are looking at the 25-year-old as a possible solution to their problems in attack, and are getting ready to launch a bid.
However the Gunners will have to act quickly to get their man, with the People claiming that Liverpool are ready to make their move.
Having reportedly made a bid for Southampton's Adam Lallana and wrapped up a deal for Bayer Leverkusen star Emre Can, Liverpool boss Brendan Rodgers is seemingly keen on getting his summer business done quickly.
The People add that Rodgers is keen on adding numbers to his forward line, with Iago Aspas set to leave the club and Fabio Borini facing an uncertain future at Anfield.
Bony is said to be keen on playing Champions League football and Swansea would be willing to sell to either Arsenal or Liverpool - only if a fee in the region of £20 million is offered however.
Liverpool rivals Everton are also said to be interested in the striker.