Suarez has reportedly drawn attention from the likes of Barcelona and Bayern Munich after a string of impressive performances, including hitting a hat-trick in today's 4-0 win over Wigan Athletic.
"Top players want to play at the top level but he's got a real affinity here within the players. He's a real leader within the group. The supporters adore him, he loves the city of Liverpool, he loves being here and he genuinely sees there's a bright future for us. It would have been easy for him last summer to have walked out, but he didn't. He's very happy," said Rodgers.
"Of course, we know all players want to play at the top level, but hopefully he can see that for us over the next couple of years. I am very confident we can keep making the strides forward and keep adding quality to our group and eventually we can get there. I don't have any issues with Luis at all on this matter. I sit here with great confidence that he'll stay.
"There will always be interest in top players, and he's a world-class player, there's absolutely no question about that. I speak regularly with Luis and I had a good meeting with his agent a couple of weeks ago, who expressed it from his perspective as well how happy the player is and how much he wants to be a part of the vision here going forward."
Suarez is currently the top scorer in the Premier League, having netted 21 times this season.