Ukrainian parliamentary sources familiar with the issue told the Izvestiya paper that the motion had been initiated by a coalition of parties and filed with the parliament at the end of the spring session.
Evgeny Balitchi, a lawmaker with the Opposition Bloc party, confirmed that the ruling coalition, which has been divided along many fault lines, was prepared to slap travel curbs on Russians.
"They have a very strong incentive to make use of their voters’ [anti-Russia] sentiment and the anti-Russia topic… They will easily impose a visa regime to hold on to power," he told the paper.
President Petro Poroshenko announced last month that Ukrainian border guards would use biometric technologies to identify foreign travelers. National security chief Oleksandr Turchynov emphasized the measure was aimed primarily at Russians.
Tighter border controls in Ukraine could prompt similar restrictions for Ukrainians coming to Russia. Russian presidential spokesman Dmitry Peskov has warned Kiev that Moscow will act reciprocally.