Suarez's future at Liverpool was the subject of constant speculation during the summer window, with the player angling for a move away in search of playing in the UEFA Champions League.
Liverpool rejected two bids from Arsenal for the Uruguayan and the striker has moved on from the transfer saga to score six Premier League goals in five matches since returning from suspension.
Suarez scored the first Premier League hat-trick of the season in Saturday's win over West Brom to spark fresh speculation that Liverpool could face a fight to keep hold of him when the January transfer window opens.
However, Rodgers has rejected talk that Suarez is likely to be on his way.
"No, I wouldn't say that," insisted Rodgers. "I think he, like ourselves, wants to be at the very highest level he can be.
"And you can see by his performances he deserves to be looking at that level.
"But it also shows he has been excellent in his attitude, you see his work rate - that is the key."
Rodgers added: "For me, this is the place for Luis. I still maintain that even if we were in mid-table this would be the place for him to be because this is a massive club - a global institution.
"But as a football club and as a team we are growing - and he can grow with us. Luis has the support of everyone at the club and the love of everyone and because this is a worldwide institution, there is no better place for him to grow.
"When a player is happy and working well you get a performance like you did [against West Brom]."
You can watch Liverpool's next game live on Sky Sports - they travel to Arsenal for next weekend's Saturday Night Football, Sky Sports 1HD at 5pm