Suarez's future at Anfield is in real doubt after he said in an interview in his home country that he was seeking a "change in environment" amid reports of interest from Real Madrid.
The striker has also accused the English press of hounding him out of the country and claims to have told the club and Brendan Rodgers of his feelings - even if he has stopped short of categorically saying he will leave Liverpool.
Now Liverpool have responded by making clear they have no intention of selling the player who scored 30 goals in all competitions last season, but ended the campaign in disgrace after receiving a 10-game ban for biting Chelsea's Branislav Ivanovic.
"Luis Suarez is not for sale," the club said in a statement. "Neither Luis or his representatives have communicated these feelings directly to Liverpool Football Club.
"The club remains supportive of Luis and expect him to honour his contract. We will not be making any further comment at this stage."
Suarez cast further doubt on his future on Thursday night when suggesting in a press conference in Montevideo that he is looking for a new club.
"I do not know when I'm going and I do not know if I'm staying," said Suarez.
"Obviously the club want me to stay, but I've talked to the coach (Brendan Rodgers) and he knows what I want. He was a player and my team-mates understand that my situation is difficult. It's a good moment for a change of environment because of all I've been through in England, where I haven't been judged as a player but based on other things.
"I have only words of thanks to the club, the fans of Liverpool, but the treatment I received from the rest of England in recent weeks has been tough. It (Liverpool) is a spectacular club, but they are aware of the way that the press treats me".