Russian leader Vladimir Putin and Ukrainian President Petro Poroshenko discussed Saturday a possible exchange of prisoners.
"Special attention was paid to humanitarian issues including an exchange of people being held" by both sides, the Kremlin said in a statement following the rare phone conversation between the two leaders.
Putin stressed that Russian journalists arrested in Ukraine should be released immediately, the Kremlin said, adding that the conflict in eastern Ukraine was also discussed.
Poroshenko for his part stressed that Sentsov, who has been on hunger strike since May 14, and other "Ukrainian political prisoners" should be released "as soon as possible".
"The head of the Ukrainian state drew attention to Ukrainians' hunger strikes and expressed concern over their deteriorating health," his office said.
Both Moscow and Kiev said that rights ombudsmen would visit the two countries' prisoners "in the near future". No other details were provided.
Sentsov, who is serving a 20-year sentence on terrorism charges in Russia's far north, is demanding that Moscow release dozens of Ukrainian political prisoners languishing in Russian prisons.
His supporters said the father of two was prepared to die in prison, clouding Russia's chance to shine on the world stage during the World Cup which begins on Thursday.
Putin and Poroshenko spoke on the phone ahead of talks Monday in Berlin between the Russian and Ukrainian foreign ministers that will also involve Germany and France.
The Berlin talks are aimed at reviving a stalled peace process in eastern Ukraine. Efforts to put an end to the four-year conflict between Ukranian government troops and pro-Russian rebels have come to a halt. The conflict has claimed more than 10,000 lives since 2014.
On Friday, Poroshenko met with relatives of Ukrainians being held by Russia including Sentsov's cousin Natalya Kaplan, promising that the issue of "hostages" would feature high on the agenda of the Berlin talks, Kiev said.
"We have already agreed and coordinated our position, the French and German sides are supporting us," Poroshenko was quoted as saying by his office.
Kiev said it was ready to exchange "23 Russians who were conducting spying activities in Ukraine".
According to Kiev's estimates, Russia is currently holding around 70 Ukrainian political prisoners.
Sentsov's lawyer Dmitry Dinze said he did not know if any backdoor negotiations were under way between Russia and Ukraine but called the phone conversation between the two leaders a good start.
"The ice has been broken," he told AFP.
Dinze, who visited the imprisoned Ukrainian director earlier this week, said doctors had threatened to soon begin force-feeding him.
"Doctors told him that irreversible consequences (of the hunger strike) can begin soon," he added.
Sentsov has already lost around eight kilogrammes, his lawyer said. He agreed to be administered a glucose drip but the protest puts him at great risk of kidney failure.
Andrei Kolesnikov, an analyst with the Carnegie Moscow Center, suggested that Putin might be considering Sentsov's release ahead of the World Cup.
"Sentsov's situation is serious because of his hunger strike and apparently there's a desire to solve the problem," Kolesnikov told AFP, adding the Kremlin did not want the Ukrainian filmmaker's protest to overshadow the football tournament.
"The World Cup should demonstrate Putin's soft power and not his cruelty."
Earlier this week Putin appeared to dismiss the possibility of exchanging Sentsov for Kyrylo Vyshynsky, a Russian state news agency journalist detained in Ukraine on treason charges.
Sentsov's supporters have launched a global campaign to secure his release, staging protests in dozens of cities in Europe, the United States and the Middle East.
Ukrainian activist Oleksandr Kolchenko, who is serving a 10-year sentence in a Russian prison after being convicted of terrorism together with Sentsov, also launched a hunger strike in solidarity with Sentsov.
He however halted his protest earlier this week due to his poor health.