But the Kremlin leader indicated that backdoor negotiations were apparently underway, raising hopes for the release of dozens of prisoners including Sentsov, who is on a high-profile hunger strike at a high-security prison in Russia's far north.
"It's so far premature to say how this issue will be solved," Putin told reporters at a summit in the Chinese city of Qingdao, adding he would not want to comment for now "so as not to violate anything here and not to disrupt anything."
Putin and Ukrainian leader Petro Poroshenko discussed a possible exchange of prisoners in a rare phone call Saturday and agreed that officials from the two countries would visit their prisoners "in the near future".
Putin said Poroshenko initiated the discussion, Presstv reported.
Fears have grown in recent weeks that Sentsov, a 41-year-old Ukrainian director and author who is serving a 20-year prison sentence on terrorism charges in Russia, could die behind bars.
He went on hunger strike on May 14 to demand Russia release dozens of Ukrainian political prisoners, timing his protest to coincide with the month-long football extravaganza that begins on Thursday.
The father of two said he was ready to die in prison, drawing comparisons with Soviet-era dissident Anatoly Marchenko, who starved himself to death in prison in 1986 after he demanded Moscow release prisoners of conscience.
'I will not back down'
Sentsov, who has agreed to be administered a glucose drip, has already lost eight kilograms and doctors have threatened to soon begin force-feeding him, his lawyer Dmitry Dinze has told AFP.
In letter to rights activists released on Saturday, Sentsov said he felt "normal" and that he had recently been transferred to the prison infirmary and given a separate room.
"So now I am a sick prisoner and not just a prisoner. :)) ", he wrote in the letter, a copy of which was published by Ukrainian TV channel Hromadske.
"Everyone understands that I will not back down."
Ukraine's rights ombudsman Lyudmyla Denysova said on Friday that Kiev and Moscow were in the process of agreeing lists of prisoners and other details.
She would inform Poroshenko of the date she would travel to Russia to visit Ukrainians on Monday, her office said.
Moscow's ombudsman Tatyana Moskalkova told Russian media for her part that she would visit Ukraine no earlier than Wednesday, a day before the World Cup begins in Russia.
Kiev said it was ready to exchange "23 Russians who were conducting spying activities in Ukraine".
According to Kiev's estimates, Russia is holding around 70 Ukrainian political prisoners.
Sentsov, who is also a pro-Ukrainian activist, was detained in Crimea in 2014 after Russia annexed the peninsula.
Rights activists have urged Putin to release Sentsov and other Kremlin critics in the spirit of the unifying sporting tournament.
Putin and Poroshenko spoke on the phone ahead of key talks Monday in Berlin between the Russian and Ukrainian foreign ministers that will also include German and French diplomats.
The talks are aimed at reviving a stalled peace process in eastern Ukraine.
Efforts to put an end to a four-year conflict between Ukrainian government troops and pro-Russia fighters that has claimed more than 10,000 lives since 2014 have come to a halt.