The France Info radio station said the pair had been detained on the Ukrainian border late on Sunday.
"Our consul has gone to the Ukrainian border to make sure that it is them," embassy spokesperson Irina Zvonova told RIA Novosti by phone, adding that, "It is likely that this is the case."
Elise Andre, who has Russian and French citizenship, was snatched from her 51-year-old father, Jean-Michel Andre, in southern France on March 20. The Frenchman was also severely beaten in the incident. He claimed that one of his three attackers was his former wife, Irina Belenkaya.
French police subsequently organized an international man hunt for Belenkaya. If arrested outside Russia, she could face up to three years in prison. However, under Russian law, she cannot be extradited.
A source in the Russian Foreign Ministry confirmed it had been informed that Belenkaya and her daughter were being held in Hungary, and that it was verifying the news.
"At the moment, this information is currently being checked by our embassy in Budapest, but work is being hampered by the fact that most government agencies in Europe are closed for Easter," Foreign Ministry spokesman Igor Lyakin-Frolov said.
The girl's father, Jean-Michel Andre, arrived in Budapest early on Monday, France Info said. The girl is now due to return to France with her father in the next few days.
The estranged couple has been embroiled in a "tug-of-war" for custody of their daughter for two years, with Russian and French courts siding with their nationals in the dispute.
Andre was awarded custody by a French court following the couple's divorce in 2007. After his wife left the country, taking her daughter with her, a warrant for her arrest was issued in 2008.
Belenkaya was subsequently awarded custody of Elise by a Russian court the same year.
In response, Andre hired private detectives to trace his wife and child. He then traveled to Moscow to seize his daughter and take her back to France. A Russian court subsequently issued a warrant for Andre's arrest.
