The Premier League champions had been linked with a £40 million January move for the Uruguayan striker, but he has now reaffirmed his desire to stay at Anfield
The Uruguayan has been in fine form so far this campaign, notching 11 goals in 16 appearances, despite Brendan Rodgers' men suffering a mixed start to the season.
Suarez's recent performances had led to suggestions that Roberto Mancini was set to test the Reds' resolve with £40-million January bid, but the forward has now underlined his commitment to the Anfield side.
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"Now I'm here, it's all about enjoying myself and trying to be here for as many years as I can, because I'm at a club where I'm very happy, my family is happy, I've got fantastic teammates and a manager from whom I'm learning so much.
"As a player, it's vital to have the backing of your manager and so I think that the confidence Brendan is showing in myself and the team as a whole is very important and it's down to us to repay that trust out there on the pitch.
"Let's hope we can keep improving. I'm working well and I'm very happy at a club where I've always wanted to be. At a club to whom I'm very grateful for the trust everyone is showing in me - a club with amazing supporters and teammates who are all great people.
"The other important thing is that the squad is very united. In spite of not getting the results we would have liked, we have a great spirit of togetherness and let's hope we can continue to pick up points."
The 25-year-old has regularly been subjected to booing from opposition supporters, largely due to his eight-match ban for racially abusing Patrice Evra last season.
But he insists that such things do not affect him and went on to hail the support he has received from Liverpool fans since joining the club.
"I think you need to really know a person before you criticise them or speak out about them," he continued.
"I think sometimes the opposition fans are more interested in booing Luis Suarez for the problems he had or because he's gone down for something than they are in their own team!
"I think that each set of supporters should just worry about their own team and leave their opponents well alone, just like the Liverpool fans do.
"I think our fans are the perfect example and always show how to help the team by wanting to get behind the side. It doesn't matter who the opposition are, the only thing they want is for their team to win by giving a lift to the players with their support.
"That's what the other clubs' fans need to do - get behind their own side and not just think about Suarez, because all that does is motivate me even more to do well."
The Salto-born forward scored the equaliser in the Reds' 1-1 draw with Chelsea on Sunday, but insists nothing but three points will do when Liverpool take on Wigan at Anfield next time round.
"Chelsea was a result that was neither good nor bad," he added. "I guess we really need to be picking up as many points as we can, given that we haven't got as many points on the board that a club like Liverpool would expect to have at this stage.
"Wigan is an absolute must-win fixture. It's a very important game for us to gain in confidence for the matches ahead and to get stronger here at Anfield, which is where we need to make the difference."