Turkey has strongly criticized Russia's invasion of Ukraine but opposes sanctions imposed by its NATO allies on principle.
"If Russian oligarchs ... or any Russian citizens want to visit Turkey of course they can," Cavusoglu said in response to a question at the Doha Forum international conference.
"If you mean whether these oligarchs can do any business in Turkey, then of course if it is legal and not against international law, I will consider it," he said, adding: "If it is against international law then that is another story."
Two superyachts linked to Russian billionaire Roman Abramovich have docked in Turkish resorts.
Western governments have targeted Abramovich and several other Russian oligarchs with sanctions as they seek to isolate President Vladimir Putin and his allies over Moscow's invasion of Ukraine.