This review examines information from systematic reviews and meta-analyses, research studies, and case reports to present current knowledge about liver damage in pregnant patients having Covid-19 during pregnancy. Problems with diagnosis and differential diagnosis are examined in the context of the need to rule out other causes of liver dysfunction, including pregnancy-related liver disease. In this paper we give an overview of COVID-19 liver problems during pregnancy. Mechanisms of liver involvement in COVID-19 infection are being examined. An overview of the assessment of abnormal liver biological syndromes in pregnant patients is provided. Differential diagnostic algorithms for primary liver damage established in a pregnant woman in the context of the Covid-19 pandemic are presented. Challenges in diagnosis and etiology assessment methods and customized management options are described. The management of pregnant women with hepatic dysfunction onset on the Covid-19 background and subsequently aggravated is discussed. The importance of anticoagulant therapy as an essential measure of symptomatic management of Covid-19 in pregnant women is emphasized, as both pregnancy and COVID-19 are thrombogenic. Hypercoagulability appears to adversely affect the pregnant women liver with Covid-19 and post Covid-19 and anticoagulant therapy has benefits in the management of liver damage associated with Covid-19. The COVID-19 liver problems in a 33-year-old woman who was not vaccinated for Covid-19, without a history of chronic liver disease, was tested positive for Covid-19 at 33 weeks of gestation is discussed. The report of the diagnostics, differential diagnosis, and management questions in the context of liver dysfunction manifested by a significant increase in alanine aminotransferase cytolysis syndrome. The positive effect of anticoagulant therapy in resolving cytolytic syndrome is emphasized. The good maternal and perinatal result is also mentioned.