Berezovsky - wanted by Moscow on fraud charges - has said he plans to move from his political asylum in Britain to Ukraine.
Media in Ukraine have speculated that he might time his arrival with Saturday's planned visit by Russian President Vladimir Putin, and the Interfax news agency reported that Berezovsky had applied for a visa.
"The Interior Ministry will face a problem that cannot be solved" if Berezovsky is allowed into the country, Interior Minister Yuriy Lutsenko said.
Interfax quoted an official in the Foreign Ministry's consular department, Mykola Tochytskiy, as saying that Berezovsky applied for a visa a week ago, but that the application did not specify when he wanted to come or for how long.
Lutsenko said the situation presented a dilemma for his country because Russia and Ukraine have an extradition agreement, but Ukraine also has a duty to protect political refugees.
"These two conventions were concluded a long time ago, but both have equal force for Ukraine," Lutsenko said.
"So not to be in a delicate situation, I'd like to propose that a political decision be made at the Foreign Ministry level."
"If Ukraine is truly independent, it will simply ignore the objections of Russia. If not, the country is still a satellite of Russia"
exiled Russian tycoon
No one could immediately be reached for comment at the Foreign Ministry.
Berezovsky, a fierce political opponent of Putin,
has been charged with embezzlement of funds from Aeroflot, Russia's top air carrier. He has rejected the charges as politically motivated.
Moscow has said it expects Kiev to hand over Breezovsky if he arrives in Ukraine.
Any attempt by Berezovsky to travel to Ukraine would present a problem for the country's new President Viktor Yushchenko, who has pledged to bring the country closer to the West but does not want to inflame tensions with huge neighbour Russia.
Former Kremlin insider
Berezovsky, a one-time Kremlin insider who retains control
of media outlets in Russia and is active in Russian politics behind the scenes, said shortly after Yushchenko's inauguration in January that he wanted to move to Ukraine.
Putin says Berezovsky should
stand trial in Russia
He said at the time that he wanted to live in a familiar environment, closer to Moscow and the culture in which he grew up.
Speaking in London, Berezovsky criticised Lutsenko's statement and challenged Ukraine to allow him to enter the country.
"If Ukraine is truly independent, it will simply ignore the objections of Russia. If not, the country is still a satellite of Russia," he said.
He said he could not travel to Ukraine without a visa, "but I don't see any reason that they won't eventually give me one".
Berezovsky has a Russian passport, but he also has refugee
documents issued from Britain under the name Platon Elenin.