Kommersant said Zakayev had dismissed the claims made by Russia's Federal Security Service (FSB) that he "has been attempting to revive the militant movement" in the North Caucasus, adding he was even ready for talks with President Ramzan Kadyrov.
"We have repeatedly stated that we're open for dialogue with any party concerned, including Ramzan Kadyrov's representatives," he told the paper.
A Kadyrov spokesman said Chechen authorities were also ready for dialogue with Zakayev.
"Ramzan Kadyrov has through the media urged Zakayev to return to his homeland and thus contribute to the revival of the Chechen Republic," said Lema Gudayev, head of Chechnya's information and analysis administration.
Gudayev stressed that Zakayev had "rejected terrorist methods of resistance" and was not linked to any serious crimes.
He also said attempts to smear "one of the most sober representatives of so-called Ichkeria" were aimed at foiling Grozny's efforts to ensure the return of political refugees. Ichkeria is the name separatist Chechens use for the republic.
The FSB said on Tuesday that a Zakayev emissary, who was in Russia's North Caucasus to revive the militant movement, had been killed by Russian forces.
Isa Khadiyev, a militant and Muslim religious leader, had been active in Chechnya and Daghestan since May 2008 reviving separatist groups controlled by Zakayev, the London-based head of the "Chechen government in exile," the FSB said in a statement.
In the Kommersant article, Zakayev denied any direct contact with Khadiyev.
Russia has repeatedly asked Britain to extradite Zakayev, accused of terrorist activities, but the request has invariably been refused.