It is unclear whether the reports of Shaimiyev's impending demise -- and his replacement with Russia's current interior minister, Rashid Nurgaliyev -- are true.
In Putin's Russia, however, such media speculation rarely happens by accident.
If rumors of Shaimiyev's ouster prove true, it would mark a spectacularly fast fall from grace. Not long ago it looked like 2007 was shaping up to be a banner year for the Tatar president.
When Shaimiyev celebrated his 70th birthday in January, Putin traveled to Kazan to honor him.
And when Putin conducted a high-profile visit to the Persian Gulf region weeks later, Shaimiyev was a key member of his delegation.
Shaimiyev has long been a powerful Kremlin ally, but one who enjoys a level of independence unusual in Russia.
In the past, his free-thinking ways were largely tolerated because of his ability to deliver the votes of his republic's 2.7 million registered voters straight to the Kremlin's doorstep.
Now, with federal parliamentary and presidential votes looming in December 2007 and March 2008, observers say some in the Kremlin no longer seem certain that Shaimiyev can provide the goods.
"They don't think Shaimiyev is sufficiently reliable for the elections to the State Duma and for the presidency," said Rashit Akhmetov, the editor in chief on the independent "Zvezda Povolzhya" newspaper in the Tatar capital, Kazan. "Shaimiyev plays too independent a political role. He tries to bargain for political position with the federal center. Such things will not be forgiven."
Akhmetov and other analysts say members of the Kremlin's so-called liberal camp -- like First Deputy Prime Minister Dmitry Medvedev, a likely presidential candidate in 2008 -- still favor keeping Shaimiyev in office.
But those Kremlin officials close to the security services, or siloviki, want him out, so that their strategic ally, Nurgaliyev, can help deliver the vote in favor of their preferred candidate -- in this case, First Deputy Prime Minister and former Defense Minister Sergei Ivanov.
Akhmetov says what was once accepted as Shaimiyev's independent streak is now seen as a sign of potential disloyalty.
"I think we'll see a change at the end of March -- General Nurgaliyev for Shaimiyev," he said.
The first sign of trouble came on February 21, when the Federation Council rejected a power-sharing agreement between Tatarstan and Russia's federal government.
Shaimiyev had lobbied hard for the agreement, which had already been approved by the State Duma. Its rejection by the upper house of parliament was a serious blow to his authority.
Tatarstan has enjoyed a wide degree of political and economic autonomy unmatched by any other Russian region.
The power-sharing agreement , despite imposing new restrictions, would have preserved the Tatar language's dominance in the republic and maintained its unmatched autonomy within Russia.
Observers have said the rejection of the agreement reflected Kremlin fears the deal would encourage separatist sentiment elsewhere in Russia. If Shaimiyev is ousted, it may be in part because of his steadfast insistence on autonomy from Moscow.
Nikolai Petrov, a specialist on Russian regional politics at the Moscow Carnegie Center, said Shaimiyev's ouster may be meant to send a strong signal to other leaders in the regions struggling to break free of Moscow's leash.
"Shaimiyev is one of the main figures among the regional leaders. What happens with him and with Tatarstan's political elite is very significant and revealing," Petrov said. "I think it's possible to remove Shaimiyev, but only after making a friendly agreement with him."
In such a case, Petrov says, he would likely be replaced by somebody close to him -- like Farid Mukhametshin, speaker of the republican legislature, or Rustam Minikhanov, Tatarstan's prime minister.
Petrov says bringing in Nurgaliyev -- who, despite being an ethnic Tatar, does not speak Tatar and is seen by locals as a Moscow insider -- would be a very risky and confrontational move.
"It seems to me that given Tatarstan's high importance in every area -- including the number of voters there -- to start a serious conflict with the regional political elite would be simply stupid," Petrov said.
(RFE/RL's Tatar-Bashkir Service contributed to this report.)
Russia's Changing Face
THE COMING MUSLIM MAJORITY: On February 28, Russia expert PAUL GOBLE, vice dean of social sciences and humanities at Concordia-Audentes University in Tallinn, Estonia, gave a briefing at RFE/RL's Washington office. Goble said ethographers predict Russia will have a Muslim majority "within our lifetime." Since 1989, Russia's Muslim population has increased by 40 percent, Goble said, rising to some 25 million self-declared Muslims. He said 2.5 million to 3.5 million Muslims now live in Moscow, gving Moscow the largest Muslim population of any city in Europe. Russia today has more than 8,000 mosques, up from just 300 in 1991. By 2010, experts predict, some 40 percent of Russian military conscripts will be Muslims.
Goble noted that these changes have been accompanied by a "rising tide" of anti-Muslim prejudice. Public-opinion surveys reveal that up to "70 percent of ethnic Russians" express sympathy with xenophobic slogans. Goble warned that heavy-handed state efforts to "contain Islam" could backfire and cause groups to move underground, "radicalizing people who are not yet radicalized."
LISTENListen to the entire briefing (about 85 minutes):
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THE COMPLETE PICTURE: To view an archive of all of RFE/RL's coverage of Russia's North Caucasus, click here.