He was hard-pressed to say whether Korobov's successor would usher in any changes, noting the agency's policies were shaped by Chief of General Staff Valery Gerasimov, Defence Minister Sergei Shoigu and Putin.
"Of course they had a constant dialogue as a commander-in-chief and a head of one of the leading special services", Peskov said.
American officials added Korobov to their sanctions list in December 2016 for his "efforts to undermine democracy" by organizing hacker attacks.
Gen Korobov had worked in military intelligence since 1985.
The agency's structure, staff number and finances are a state secret.
It has allegedly been involved in undercover operations in Ukraine - after Russia's annexation of Ukraine's southern Crimea peninsula in 2014 - and is accused of direct involvement in the hacking of the 2016 United States presidential election.
Russian male life expectancy was 67 as of 2016, according to the World Bank.
Tass tweeted the news of his death with an image of General Korobov in a grey military jacket.
CNN's Nathan Hodge reported from Moscow and Laura Smith-Spark from London.