The Serie A club were thought to be in for £17million man Lavezzi, who they sold to PSG for £21m in 2012.
They have also been linked with Balotelli, who has fallen dramatically out of favour at Anfield.
However, club chairman Aurelio De Laurentiis has revealed the club cannot afford the Lavezzi's £3.5million yearly wages, which was the reason he left Naples in the first place.
Nor can they stump up enough cash for Balotelli, leaving Sampdoria the sole suitors of the Italy international.
Ezequiel Lavezzi Player Profile
De Laurentiis told Il Mattino: "You forget that Lavezzi has a salary of €4.5million net per year and that it was he who wanted to leave Naples. He decided (to go) in 2011, and we asked him to stay a year, so in 2012 he moved to Paris St. Germain.
"Sometimes the players' agents have fun [linking us to players], but we have nothing to do with neither Lavezzi or Balotelli."
However, the Argentine's arrival may depend on Brendan Rodgers' success in offloading Balotelli, whose transfer value has dropped further since his £16m summer arrival.
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