The Uruguayan scored the third hat-trick of his Reds career in a 4-0 win over Wigan on Saturday, taking his goalscoring tally to 21 goals in 27 Premier League appearances.
His manager was quizzed on whether the expected lack of Champions League football next term will prompt Suarez to leave Anfield, but Rodgers dismissed any chance of a summer exit.
"I don’t have any issues with Luis in that manner, I sit here with great confidence that he’ll stay,” he told reporters.
"Of course there will be interest in top players and he’s a world-class player, but I speak regularly with Luis and we had a good meeting with his agent a couple of weeks ago and he expressed from his perspective as well how happy he is.
“It’s hard to say [Champions League football] is not important because top players want to play at the top level. What he’s got is a real affinity here. The supporters adore him, he loves the city of Liverpool, he loves being here and I think he genuinely sees a bright future for us.
Wigan boss Roberto Martinez was downbeat following the heavy defeat and blamed “soft defending” on conceding four goals - taking the total conceded to 55 for the season, the most of any team this term.
He told reporters: “We see the next 10 games a great opportunity to get points, but it’s clear we need to learn some lessons quickly as the next five home games we can’t defend in the manner that we did in the first 20 minutes [today].
“We do need to improve on what we did today, that’s quite clear; if we are that soft defensively you’re going to make it very difficult to win football games.”
Emmerson Boyce and James McArthur were seen arguing on and off during the game, with a physical altercation happening when defending a corner.
And, instead of condemning any ill discipline, Martinez instead praised the passion of the pair.
He added: “If I’m honest with you, I am glad to see that because you need passion, and the position we are in we need passion.
“The players can’t accept defeat and it was a bit of frustration between players, they thought we had the opportunity to win and get three points and the reaction from McArthur and Boyce is what I want in the dressing room.”