Sky Sport 24 claimed on Sunday that the Naples outfit have turned down Zenit's bid for their star player as it falls below the striker's €30 million release clause.
An earlier report in La Gazzetta dello Sport had earlier reported that the Russian champions had submitted a bid for the Argentina international.
Lavezzi has a contract with Napoli until 2015 and has also been linked with a move to Inter Milan as they prepare to find a replacement for Anzhi bound Samuel Eto'o.
However, Napoli president Aurelio De Laurentiis hopes he can persuade Lavezzi to stay at San Paolo.
The Argentine impressed for Napoli last season, helping them to a third-place finish in Serie A and UEFA Champions League qualification.