News of the Russian club’s bid surfaced on Monday and CSKA were hopeful that it would be accepted.
However, San Lorenzo know they have a player in high demand and turned down the proposal of €8m plus a 10% sell-on clause.
San Lorenzo would accept €8m for Gaich, 21, but only with a 30% sell-on clause included.
CSKA must therefore improve their offer if they hope to sign the towering target man.
Argentine international Gaich has a €15m release clause, but will be allowed to leave for less than that.
No to Zabaleta
Zabaleta played for the Argentine club as a youngster before moving to Espanyol in Spain.
But he will not be returning home, with a San Lorenzo representative telling TyC they are well covered in that position.
Head coach Mariano Soso has three options – Marcelo Andres Herrera, Víctor Salazar and Gino Peruzzi – for the right-back position.