"We are currently discussing this issue within various departments ... we will take into account a wide range of aspects, including humanitarian ones," Rudenko was cited by local media as saying.
"We do not want to complicate the lives of those Ukrainian citizens, who wish to leave the country and go to Russia. Obtaining visas would become difficult for them," he said.
Rudenko said that a final decision has not yet been made, and that the response would not have to be symmetrical.
In an earlier statement on Tuesday, Rudenko said Ukrainian citizens could still enter Russia without a visa until Jan. 1, 2023.
On July 1, Ukraine introduced a visa regime for Russian citizens following a decision by its government.
Ukrainian President Volodymyr Zelensky said in June that the country had decided to end visa-free travel for Russian citizens due to the "unprecedented threats to the national security, sovereignty and territorial integrity" of Ukraine.