The Russian and Ukrainian leaders have had a telephone conversation over the fate of jailed high-profile prisoners, raising the possibility of a swap.
The call came after Ukraine jailed two alleged Russian special forces soldiers for several crimes including terrorism.
Yevgeny Yerofeyev and Alexander Alexandrov are accused of involvement in Ukraine’s conflict with pro-Russian rebels in the east.
A Russian court jailed Ukrainian Nadiya Savchenko for 22 years in March.
She was captured by eastern separatists in 2015 and accused of directing artillery fire that killed two Russian journalists.
Relations between Russia and Ukraine badly deteriorated following Moscow’s annexation of the Crimea peninsula in 2014 and its alleged support for pro-Russian rebels in eastern Ukraine.
Russian President Vladimir Putin spoke with Ukrainian counterpart Petro Poroshenko on Monday night, the Kremlin said.
During the phone call, the pair agreed Savchenko would be allowed a consular visit “in the very near future”, according to a statement.
Her trial caused an international outcry and her lawyers have said her condition has deteriorated after she started a hunger strike in protest against her treatment.
On Monday a court in Kiev found Yerofeyev and Alexandrov guilty of waging an “aggressive war” against Ukraine, committing a terrorist act and using weapons to provoke an armed conflict.
They were sentenced to 14 years in jail.
Russia has always denied sending troops to eastern Ukraine and said the men were volunteers who had left active service.
Mr Poroshenko has previously proposed swapping the two Russian men for Savchenko.