The towering 21-year-old is being linked with a number of European clubs after almost joining Club Brugge in January.
San Lorenzo are looking to sell Gaich in order to raise money and balance the books.
And CSKA have made an attractive offer that would involve an initial €8m fee with more to follow in add-ons.
The Russian club have yet to receive a response from San Lorenzo, but are confident their bid will be accepted.
Gaich has scored seven goals in 23 league appearances for San Lorenzo.
Nicknamed the ‘Tank’ because of his impressive physical stature, Gaich is a hard working target man with a good eye for goal.