The Uruguayan forward has hinted that he wants to leave Liverpool this summer, leading to speculation that he might be on his way to a club who could offer him Champions League football.
Arsenal are currently leading the chase for the 26-year-old and lodged a bid of £40m +£1 earlier this week.
But Ayre told a press conference in Thailand, where Liverpool are preparing for a pre-season friendly, that the stance on Suarez had not changed.
"The situation with Luis Suarez remains the same," said Ayre. "It's never been our intention to sell Luis.
"We have received two separate offers from Arsenal and have rejected both."
Liverpool will play the Thai national team on Sunday and Suarez will feature at some point, although he is still short of fitness, having been given time off following the Confederations Cup.
Reds boss Brendan Rodgers said: "He's three weeks in schedule behind other players.
"But one thing about Luis is he loves to play the game, he loves training and working. I'm sure at some stage of the game, he will play a part."