"With such a crazy reaction to our article, the authorities aren't ready for it," he said.
Hull said the paper admits there is no factual basis for the story.
"But it isn't hard to believe. Lately, Ludmilla Putin hasn't been seen much in public with her husband," he said.
Mr Putin has denied that he divorced his wife Ludmilla and planned a June wedding with Kabaeva.
In 2007, Kabaeva, 24, was given a new position as an MP in the Putin-controlled parliament. The former rhythmic gymnast has represented Russia at two Olympic Games.
Most Russian media obey the Kremlin line that Putin's private life is off limits.
Alexander Lebedev, the owner of Moskovsky Korrespondent, is believed to have good relations with the Kremlin but also co-owns a pro-opposition newspaper, the Novaya Gazeta, where Anna Politkovskaya, a fierce critic of Putin, worked before she was murdered in 2006.
Staff at the Moskovsky Korrespondent believe that the newspaper has been halted only temporarily.
"Editors believe the paper will be back in print shortly, surviving perhaps just long enough for the spotlight on media censorship to move elsewhere," Hull reported.