Xi Jinping may be "contingency planning" in case Putin is deposed, an analyst told Insider.
He appears to be forming closer ties to Putin's deputy, another analyst wrote.
Rumors of a military coup, as well as concerns about Putin's health, are circulating in Russia.
China's President Xi Jinping and Russia's President Vladimir Putin have sought to portray themselves as adamant allies, engaged in a longstanding partnership to roll back the US' global dominance.
But China's president may not be as convinced as he appears that his "no limits" friendship with Putin will endure, amid rumors that the Russian president is suffering from a serious illness, or may be deposed in a coup.
According to one analyst, Xi is likely already seeking to form closer relations with potential successors to the Russian president.
Anders Åslund, an economist and senior fellow at the Atlantic Council, said Xi appears to be cultivating closer ties to Russian Prime Minister Mikhail Mishustin.
At the April summit where the Chinese president visited Putin in Moscow, Xi held a rare one-on-one meeting with Mistushin, noted Åslund.
Then, in May, China's Prime Minister Li Qiang invited Mishustin to China, where he "received Mishustin at the Great Hall of the People, once again completely beyond the ordinary bounds of Chinese and Russian protocol."
"Why was Mishustin invited and not Putin? This cannot have gone down well with the Russian leader," he writes.
As evidence of Putin's displeasure, he points to Mishustin's absence from subsequent Russian Security Council meetings, of which the prime minister is a permanent member.
"This old-style Kremlinology is perhaps the best evidence we have that China may be looking beyond Putin and seeking to cultivate alternative relationships in Russia."
Mistushin's is not a name that usually comes up in discussions of potential successors to Putin. A former tax official, he has cultivated a reputation as an effective manager. According to Russian independent media organization Meduza, he has played "no part" in implementing Putin's Ukraine war, and does not discuss it.
In the closed world of Russian and Chinese politics, where reliable information on the thinking of its leaders is rare, analysts have long relied on subtle signals and snippets of information to read the underlying power dynamics.
It's a discipline that became known as "Kremlinology" during the Cold War, and is still very much alive today, with Putin's use of a huge table for meetings with top officials the subject of weeks of speculation last year about his state of mind.
The same methods are applied to the secretive world of politics in Beijing.
Reading between the lines, analysts have previously found signs of underlying tensions in Putin and Xi's relationship, such as Xi's refusal to approve a new gas pipeline from Siberia to China, which they say is a power play Xi is using to underscore Russia's new reliance on China.
Ali Wyne, an analyst with the Eurasia Group in Washington, DC, told Insider that given rumors about Putin's health, and potential challenges to Putin's power, it made sense for China to be engaged in "contingency planning."
"Governments regularly engage in contingency planning; that activity does not necessarily indicate strategic preferences," he said.
"Given ongoing rumors about Putin's health and speculation that a Ukrainian defeat of Russia could undermine his rule, many countries—including the United States and China—are likely envisioning various post-Putin futures and weighing the implications of each for Russia's domestic politics and foreign policy."
However, he cautioned, it's too early to suggest that Xi would prefer to be dealing with a different president in the Kremlin.
"Whether one considers the number of occasions on which Xi and Putin have met, however, the growing intensity of their shared grievances against US influence, and the priority that both have placed on deepening Sino-Russian relations, it seems premature for now to conclude that China seeks different Russian leadership," he said.
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