The two leaders raised the possible exchange in a phone call on Monday.
Army volunteer Nadiya Savchenko, seen as a national hero in Ukraine, was jailed by a Russian court last month.
A court in Ukraine then jailed two alleged Russian special forces soldiers for several crimes including terrorism.
Yevgeny Yerofeyev and Alexander Alexandrov were convicted on Monday of involvement in Ukraine's conflict with pro-Russian rebels in the east and 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.
Savchenko was captured by pro-Russian rebels in 2015 and put on trial in southern Russia accused of directing artillery fire that killed two Russian journalists. She was jailed for 22 years. Her lawyers have suggested a prisoner exchange could take place within weeks.
Mr Poroshenko spoke to the Russian president on Monday night, stressing that Ukraine sought Savchenko's immediate release from jail.
He told reporters in Kiev on Tuesday that "based on a preliminary plan, I think we've managed to agree a definite formula for freeing Nadiya".
"I underlined that I was ready to send the presidential plane with my representatives, in order to collect Nadiya and bring her back to Ukraine as soon as possible."
He refused to comment on the time it would take to finalise a deal, but told reporters that when human life was a stake it was important to forget politics. Savchenko has been on hunger strike in jail but her lawyers said on Tuesday that she had started drinking water again and was on a drip.
President Putin's spokesman refused to comment on the content of the phone call on Tuesday, other than to tell the BBC that he did not know whether the planned exchange would happen quickly.
Asked about a potential prisoner swap last week, President Putin told the BBC's Sarah Rainsford that the Ukrainian government had been in touch but that Russia could not "jump the gun".
After visiting Savchenko on Tuesday, lawyer Nikolai Polozov said he was hopeful that political leaders could reach a final agreement within weeks, rather than months. Another lawyer said little was likely to happen before 18 May, when the 14-year jail terms handed down to the two Russians were due to take effect.
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 during the ensuing conflict in eastern Ukraine.
Although a ceasefire is in place on the front line between separatists and the Ukrainian army, there has been a spike in violence in recent weeks.
Ukraine's President Petro Poroshenko has said he has agreed with Russian President Vladimir Putin on a mechanism to swap a high-profile Ukrainian prisoner for two Russians.