Putin has denied the allegations.
The Russian tabloid "Moskovsky korrespondent" alleges that the outgoing president secretly divorced his wife, Lyudmilla, over two months ago and will wed Kabayeva on June 15, the day Russia celebrates the Holy Trinity this year.
"His close entourage knows well that Putin, like all healthy men, is not indifferent to beautiful, sporty women," the tabloid wrote.
In an interview on national television last year, the 24-year-old Kabayeva admitted feeling torn between conflicting interests.
"I'd like to take part in Beijing," she said. "I'm a sportswoman. Of course, I'd like to win these Olympic Games. But above all, I'd like to be a good mother. I want to have children, a good family."
Kabayeva, who currently serves as a deputy in the State Duma, has since abandoned her ambitions to compete at the 2008 Olympic Games in Beijing. And according to "Moskovsky korrespondent," she is about to fulfill her family ambitions by tying the knot with Putin at a lavish wedding ceremony in St. Petersburg.
'No Right To Interfere'
"Moskovsky korrespondent," citing a source close to the director of a company allegedly participating in a closed tender to organize the wedding, claims that the ceremony will be held in St. Petersburg's Konstatinovsky Palace, where Putin hosted the Group of Eight summit in 2006.
The rumors have been the talk of Russia since their publication earlier this month. Putin's alleged affair with the attractive young gymnast, who has posed nearly nude for a number of magazines, certainly clashes with the churchgoing, family man image that he has carefully cultivated.
Putin addressed the issue for the first time after he was asked about the stories during a news conference with Italian Prime Minister-elect Silvio Berlusconi on the Italian island of Sardinia on April 18.
The Russian leader squarely rejected the allegations, stressing that he did not approve of such meddling in his private life.
Putin (right) and Lyudmilla with Austrian President Heinz Fischer
"Of course, society has the right to know about the lives of public figures, but even in this case there are certain limits," he said. "There is a private life that nobody has the right to interfere with."
Kabayeva's spokeswoman has also denied the rumors.
But the editor in chief of "Moskovsky korrespondent," Grigory Nekhoroshev, defends the article. He says reporters spent weeks checking the facts and that the public has a right to know everything -- whether true or false -- about their president.
"I am 100 percent convinced that people should know this information about leaders," he tells RFE/RL's Russian Service. "They should be aware even of rumors so that a public discussion can take place."
Sarkozy Syndrome?
Another tabloid, the website skandali.ru, has added to the intrigue by reporting that Federal Security Service (FSB) officers raided the offices of "Moskovsky korrespondent" following the controversial piece. They allegedly questioned all the journalists who had a hand in the article and detained Nekhoroshev -- a claim Nekhoroshev himself has rejected, saying the FSB officers were in reality a group of friends who had come to pick him up from the office.
By wedding Kabayeva, Putin would be walking in the footsteps of his French counterpart Nicolas Sarkozy, who recently divorced his wife and secretly married top model Carla Bruni.
But presidential romances with beautiful young women, says Russian humorist Viktor Shenderovich, tend to be about much more than just love.
"I don't think this story is about the private life of this or that person -- it's about status," he says. "This a symbol of power. Alina Kabayeva is not only a young, interesting woman. Alina Kabayeva is a symbol, including a sexual symbol."
RFE/RL's Russian Service contributed to this report