Xi, 59, has missed some meetings, including one scheduled with visiting U.S. Secretary of State Hillary Clinton, but thus far there has not been any official statement about his absence.
His lack of public face time comes as the country is preparing for this year's once-in-a-decade leadership change, during which Xi has been expected to be named president and general secretary of the Communist Party, succeeding Hu Jintao.
Speculation about his absence has spread on the Internet, from questions relating to his health to whether his political position is in trouble, The New York Times reported.
The report quoted some diplomats they'd heard Xi may have pulled a muscle while swimming or playing soccer. The report also said a well-connected political analyst in Beijing said in an interview Xi might have had a mild heart attack.
The Xi situation also comes at a time when the ruling party, seeking to project a smooth power transition to the world, has had to deal with political scandals, including that of Bo Xilai, the rising political star later deposed, and the highly publicized murder trial of his wife. The state also has been working hard to stop the economy from declining further.
The Times said it is not unusual for Chinese leaders to be absent from the public for long, but that it was not usual to cancel meetings with foreign dignitaries at the last minute.
"There's every sort of crazy rumor about Xi's health," said a senior Chinese journalist. "But no one is saying anything."
The Washington Post said Xi's cancellation of meeting with Clinton may have been Beijing leadership's reaction to the China policies of the administration of U.S. President Barack Obama.
But the newspaper said Monday's cancellation of Xi's meeting with the prime minister of Denmark raised new speculation ranging from his health to intrigue at the party hierarchy.
"You see the tension, with elite politics not changing as fast as society is changing," Cheng Li, an expert on China's leadership at the Brookings Institution in Washington, told the Post. He said there is "a lack of transparency, so we end up with all these" rumors.
Most outside analysts told the Post a health problem may be the most likely reason since with any other crisis, President Hu Jintao would probably not have traveled to Vladivostok, Russia, for the weekend Asia-Pacific Economic Cooperation meeting. However, the analysts said Xi's problem must be so serious that officials cannot even produce a current photograph of him to put an end to the rumors.
The Wall Street Journal reported Chinese and English language searches for Xi's full name and surname were blocked on Weibo on Monday but that searches for "Jinping" weren't blocked in Chinese.
"The bottom line is that there is no reliable information to go on," Kenneth Lieberthal, a former White House official now with the Brookings Institution, told the Journal. "Something is amiss -- otherwise, they would have found an opportunity for him to be seen. But whether he hurt his back or there is some other problem is something that at this point there is no way to know with confidence."
Notable deaths of 2014 [PHOTOS]