The Kremlin has been coy in recent weeks about whether the 64-year-old head of state would run for another six-year term in the March 2018 election.
In early July, his spokesman said the matter was still undecided.
Putin was on a visit to the Siberian region of Buryatia on Friday when a veteran practically begged him to consider running for re-election.
“We have a request for you. When there is the next presidential election, we all ask you to run again for this post.
“We will be very happy,” the man said in comments carried by state news agency TASS.
Putin replied curtly: “OK, I will think about it. Thank you.”
Putin served two consecutive four-year terms from 2000 to 2008, then became prime minister until 2012, when he again became president.
Shortly after his second presidential term, the Russian constitution was amended to enable the head of state to serve six-year terms.