The Italian was widely linked with a move to the Russian giants but club CEO Adriano Galliani did not hesitate to turn down their approach for him
The 26-year-old insisted the Russian giants were interested in his signature during the January transfer window, but the club's vice-president rejected the bid without hesitating.
"When Galliani informed me of Zenit’s offer he didn't even consider it," Abate told Forza Milan.
"He simply asked me to stay. He’s the person that wanted me at Milan and he’s never thought of selling me."
The Italy international went on to say that his side had also turned down an approach from Fiorentina for him when the Rossoneri won Serie A in 2011.
"In the year of the Scudetto, he even turned down an offer from Fiorentina for me."
Milan are currently two points clear of the Viola in the final Champions League place heading into the final game of the season.