The controversial striker hit the headlines on Sunday when he bit Chelsea defender Branislav Ivanovic on the arm during the 2-2 draw at Anfield.
Liverpool managing director Ian Ayre told the club's official website: "It affects his future in the sense that we have to work with him on his discipline - but Luis is a very important player to the club. He's a very popular player with his team-mates. As we keep saying, he signed a new four-year contract last summer and we'd all love to see him here throughout that contract.
"He's a fantastic player, top scorer and everything we'd want in a striker, so there's no change there."
The Uruguay international has requested his fine be donated to the Hillsborough Family Support Group, which marked the 24th anniversary of the tragedy with a service at Anfield last Monday at which Suarez was present with his team-mates.
Suarez revealed the fine on Monday via Twitter.
He said: "For my unacceptable behaviour yesterday the club has fined me today.
"I have asked the club to donate the money to the Hillsborough Family Support Group for the inconvenience I have created to the Liverpool fans and to Ivanovic."
The Uruguayan - who later went on to score a 97th-minute equaliser in the 2-2 draw - tangled with Ivanovic during the second half of the match.
No action was taken at the time by referee Kevin Friend and both managers - Brendan Rodgers and Rafa Benitez - said they did not initially see the incident.
Suarez apologised, first via his Twitter account, and then through a statement issued on the club's website.
"I am deeply sorry for my inexcusable behaviour earlier today during our match against Chelsea," Suarez said in his statement.
"I have issued an apology and have tried to contact Branislav Ivanovic to speak to him personally. I apologise also to my manager, playing colleagues and everyone at Liverpool Football Club for letting them down."
Earlier on Twitter, Suarez had written: "I'm sad for what happened this afternoon, I apologise Ivanovic and all football world for my inexcusable behaviour. I'm so sorry about it."
Suarez, famously banned for eight matches last season for racially abusing Manchester United's Patrice Evra, later returned to the social networking site to say he had spoken directly to Ivanovic.
"I've just spoken to Ivanovic on the phone and I could apologise directly to him. Thanks for accepting," he wrote.
Chelsea confirmed that had been the case with a club spokesman saying: "Luis Suarez called Branislav this evening. Branislav appreciated the call and his apology."
Ivanovic was also spoken to after complaints made to Merseyside Police were passed on to their southern colleagues, who wanted to ascertain whether the defender had sustained any injury.
That was found not to be the case and Ivanovic told police he did not want to press charges.
The matter will now most likely be dealt with by the Football Association, and Chelsea and Ivanovic will assist with any investigation should it be necessary.
Liverpool quickly also responded to the incident, which came when the two players clashed following a challenge in the Chelsea penalty area.
Rodgers had said in his post-match interviews that he had not seen the incident, but later said: "Having reviewed the video footage and spoken to Luis, his behaviour is unacceptable and I have made him aware of this."
Suarez was banned for seven matches for biting an opponent while playing for Ajax in 2010 against PSV Eindhoven in the Dutch league.