Suarez has been the subject of two bids from English Premier League rivals Arsenal, with the second an eye-catching 40 million and one pounds, British media reported earlier this week.
Liverpool managing director Ian Ayre said both bids had been rejected and the club would not welcome any further offers for the 26-year-old, who scored 23 goals last season but collected a 10-game suspension for biting Chelsea defender Branislav Ivanovic in April.
"It has never been our intention to sell Luis," Ayre told reporters in Bangkok on Friday.
"As has been widely reported in the media, we've received two separate offers from Arsenal for the player and we've rejected both offers.
"So, our situation remains the same and Luis Suarez remains a Liverpool player. He's here in Thailand as part of our squad."
Suarez had been given extended leave by Liverpool after representing his country in the Confederations Cup in June and joined up with the squad in Australia last week, playing 20 minutes in the win over Melbourne Victory on Wednesday.
Liverpool manager Brendan Rodgers said his controversial striker, who has previously served a ban for racially abusing Manchester United defender Patrice Evra, was slowly working his way back to full fitness after the break.
"He's still getting up to fitness. He's about three weeks or so behind all the other players but the one thing about Luis is he loves to play the game," Rodgers told reporters.
"He loves training and he loves working but he lives for the game of football. So, I'm sure at some stage he'll play a part."
One player who is departing Anfield is goalkeeper Pepe Reina with Rodgers confirming the Spanish stopper's loan move to Serie A side Napoli.
Rodgers said Liverpool only signed goalkeeper Simon Mignolet from Sunderland as they had expected Reina to leave on a permanent deal.
"As events transpired, that move didn't happen and it left us with two very good goalkeepers," the Northern Irishman said.
"As a senior goalkeeper, he needs to be playing. It's a very important year for him with the World Cup next year. It wouldn't have served any purpose, both for the club and him personally, if he'd been the one missing out.
"It's decided he will go to Napoli and we've got two very good goalkeepers still at the football club. We'll review it after the loan finishes."
After Sunday's game against Thailand, Liverpool will return to Europe to play final friendly matches against Olympiakos, Valerenga and Celtic before opening their Premier League campaign against Stoke City on August 17.
(Writing by Patrick Johnston in Singapore; Editing by Peter Rutherford)
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