Reports have suggested Manchester City are weighing up a £40 million bid for the Uruguay international when the transfer window reopens.
But the Uruguayan responded to the rumours by re-iterating his happiness at his current club, hours after both boss Rodgers and City themselves played the suggestions down.
"I have a very long contract here and it's a dream come true to be playing at a club like Liverpool because, as I've said, as a boy I dreamt of playing for a team like this," Suarez said via the Liverpool website.
"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 team-mates 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 team-mates 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."
City have distanced themselves from the link, with club sources claiming there are no plans for a move for the 25-year-old, but in any case Rodgers stressed he has every intention of hanging on to his leading scorer and only fit senior striker.
"There will be no bidding war. He's staying here," said the Northern Irishman. "If we lost Luis then we've got no strikers. I don't think we can afford to lose anyone.
"He's certainly not someone we want to sell or move on. He's been a brilliant player to work with and we want to add to our squad, not take people out of it, especially a world-class player."
Suarez only signed a new long-term contract in the summer and while Rodgers knows he needs to strengthen his forward line in January he does not believe he has to do so in order to convince the South American to stay.
"We just continue to work and stay focused on what we try to achieve," added the Reds boss. "Luis has already shown in the summer his commitment to the club, he's signed a new deal."