Appiah, who is currently in England on attachment with Manchester City, says the presence of these two top players will boost the Black Stars squad.
Essien, who plays for Real Madrid, asked not to be considered for the 2013 Africa Cup of Nations as he was recovering from two serious knee injuries.
The midfielder was struggling to return to his best form as his place in Chelsea was left shaky before he secured the loan move to Real Madrid.
AC Milan’s Boateng quit Ghana in 2011 citing health reasons. Some Ghana FA official and Appiah have visited Boateng in Milan to ask him to reconsider his decision without success.
Despite that, coach Appiah has not given up hope in persuading Essien and Boateng to play for the Black Stars again.
“I would love to have every good player available and Boateng and Essien are both fantastic players,” said Appiah.
“We are still talking to them to get them to join the team.”
Ghana will play a 2014 World Cup qualifier away to Sudan in June and Appiah’s side must win to keep the pressure on Zambia, who are a point above them at the top of Group D.