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.
The squad listed on the website on Tuesday initially featured 28 names, but that of Daniel Pacheco has since been removed, with the club subsequently confirming the Spanish forward would not be travelling.
Pacheco is not injured and no further information has been given as to the reason for his withdrawal.
On Monday, Liverpool managing director Ian Ayre gave his views on the Suarez situation, and stressed the need for everyone at Anfield to show their support for the Uruguayan as they seek to keep him at the club.
"He only needs to do what he did last season and everyone will feel he's in the right place," said Ayre. "He should carry on getting the support that he deserves and gets from Liverpool."
Last week, Brendan Rodgers explained how the club was in 'constant communication' with Suarez.
Rodgers told talkSPORT: "We communicate in some way nearly every day, either through text or conversations.
"At the minute, he is on a break, he is relaxing with his family. He has got three years left on his contract, we don't want to sell him, and we hope everything will be fine for the summer."