“We have official estimates from the General Staff … And they range from 10,000 … to 13,000 dead,” Mykhailo Podolyak told Ukraine's Channel 24 on Thursday.
Mr Zelenskyy will make the official data public “when the right moment comes”, he added.
In June, as Russian forces battled to take full control of the easternmost Luhansk province, Mr Zelenskyy said Ukraine was losing “60 to 100 soldiers per day, killed in action, and around 500 people wounded in action”.
Russian Defence Minister Sergey Shoigu said in September that 5,937 Russian troops had been killed in the nearly seven months of fighting to that point.
Both sides are suspected of downplaying their losses to avoid damaging the morale of their troops.
Top US general Mark Milley last month said more than 100,000 Russian military personnel have been killed or wounded in Ukraine, with Kyiv's forces likely to be suffering similar casualties.
Those figures — which could not be independently confirmed — are the most precise to date from the US government.
Thousands of Ukrainian civilians have been killed in the worst fighting in Europe in decades.