He will replace James Salinsa Debbah who has said he is resigning for the second time in a month after criticisms of his inability to beat Togo at the Antoinette Tubman Stadium in Monrovia in the 2017 Africa Cup of Nations qualifiers.
Appiah is the current in charge of Sudanese top-flight side Al Khartoum SC.
"A lot of young Liberian players will find success under Appiah,” a Liberian Football Association source spoke on the condition of anonymity to the New Liberian.
"A lot of young Liberian players will find success under Appiah.
"He is someone we think we can work with given his immense experience and technical abilities. He is definitely a good coach."
Appiah qualified and coached Ghana at the 2014 FIFA World Cup finals in Brazil.