Brendan Rodgers has identified the Ivory Coast striker as the man to replace Suarez, according to the Daily Mirror.
In his first season in British football after a £12m move from Eredivisie side Vitesse Arnhem, the 25-year-old scored 25 goals for Swansea - 16 of those came in the Premier League.
Bony, who scored twice for the Ivory Coast in the World Cup, has a £19m release clause and has told friends he is 'desperate' for a move to Anfield, according to the report.
West Ham and Tottenham were previously interested in the striker, but are said to have been put off by the hefty pricer tag.
Liverpool transfer targets: Who might they sign this summer?
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However, Swansea chairman Huw Jenkins told the Daily Mail that he had not yet spoken to anyone from Liverpool about a potential move.
"I have no idea about that. The only thing I'd say is I'm completely unaware of contact between Liverpool and myself," an angry Jenkins told the paper.
"I was very surprised to hear and disappointed to hear that Liverpool had gone down that route and were talking to the player behind behind my club's back."
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