Suarez - who will miss the start of the season as he completes a 10-game ban for biting Chelsea's Branislav Ivanovic in April - has said several times that he is unhappy in England.
However, his club have stressed the Uruguay international is not for sale and have named the 26-year-old in their touring party - although he is not due to link up with his team-mates until mid-way through the trip.
Suarez, defender Sebastian Coates and goalkeeper Pepe Reina have been given an extended break by manager Brendan Rodgers following their involvement in the Confederations Cup in Brazil.
The rest of the squad, which will fly out on Tuesday, includes new signings Luis Alberto, Iago Aspas, Kolo Toure and Simon Mignolet as well as captain Steven Gerrard, who signed a two-year contract extension on Monday.
Liverpool are due to take on an Indonesia XI in Jakarta on July 20. They will then face Melbourne Victory in Australia on July 24 before wrapping up the tour against Thailand in Bangkok on July 28.