The Frenchman was signed by the Gunners from Lyon for a then club-record fee of £46.5million in 2017.
Lacazette is in his third season at Arsenal and the Gunners are not thought to be interested in selling.
Nonetheless, Cheltsov claims he put forward the signing of the forward to the Russian Premier League side, but they ended up landing Malcom for £36m from Barcelona instead.
He also claims the 28-year-old has a £61m release clause in his contract with the north London club, although this is not believed to be the case.
“I offered Alexandre Lacazette to Zenit,” Cheltsov told Sport Business Gazeta.