The family friend, whose identity was not reported, said the 35-year-old TV presenter is facing an "awkward divorce" following the birth of her first child, The Telegraph on Sunday said.
"It is a very complicated situation," the friend said. "Everyone is just being as supportive as they can, but splitting up with your husband at the same time as you have a baby could not be worse. It may be an awkward divorce."
Tolstoy, whose late distant relative wrote the classic book "War and Peace," married her 45-year-old husband Shamil in 2003 after meeting him on a horseback trip.
The Telegraph said Tolstoy confessed in 2008 the couple's relationship had been tested when she spent a month traveling as part of the BBC series "Horse People with Alexandra Tolstoy."