Liverpool managing director Ian Ayre said there was no change in his side's stance after they knocked back Arsenal's second offer of 40 million pounds ($61 million).
"The situation is the same," Ayre told reporters in Bangkok. "We do not intend to sell him (Suarez). Nothing has changed." He added that Liverpool had received "two offers from Arsenal and they had both been rejected".
Liverpool rate Suarez, the Premier League's second highest scorer last season, in the same category as fellow Uruguayan Edinson Cavani, who moved from Napoli to Paris Saint-Germain for a French-record 64 million euros (55 million pounds, $84 million).
Liverpool owner John W. Henry tweeted "What do you think they're smoking over there at Emirates?" referring to Arsenal's home ground, after their latest bid was revealed this week.
Losing Suarez would put a major dent in Liverpool's hopes of challenging for a Champions League spot this season. But the Uruguayan, who wants to be assured of playing in Europe's top competition, has spoken openly about a move.
This week, manager Brendan Rodgers told Suarez he should show loyalty to Liverpool after they "stood by him, like a son" during a racism controversy and also a biting incident, for which Suarez is still serving a 10-match ban.
Rodgers said Suarez, who came on towards to huge acclaim towards the end of Liverpool's friendly on Wednesday in Melbourne, was likely to play some part in Sunday's game against Thailand in Bangkok, "if he is fit".
"He's three weeks behind the others in fitness training, but he simply loves playing," Rodgers said of Suarez, who only joined the tour from Montevideo this week. "I am sure he will play for a while."
Rodgers said Liverpool received a "humbling" reception as they arrived in Bangkok for the final leg of their tour, after wins in Jakarta and Melbourne.
He added that he was pleased with his defence -- yet to concede a goal so far on tour -- despite the retirement of Jamie Carragher, and praised centre half Kolo Toure, newly arrived from Manchester City.
"He's a quality player and a terrific person. Supported by players like (Daniel) Agger and (Martin) Skrtel we have a good defensive line," said Rodgers.