The Uruguay international is enjoying an outstanding season, having scored 20 goals so far, but that has led to speculation that other clubs could move in for the £40million-rated forward if the Reds' absence from the UEFA Champions League continues.
Liverpool are currently seventh in the Premier League and facing a battle to regain a place in Europe's elite competition.
But Rodgers does not believe the 26-year-old's future on Merseyside depends on whether they qualify or not.
Rodgers said: "Luis had a terrific season last season and he had an opportunity to leave in the summer, and probably would have had a ready-made excuse with a new manager coming in, but he never did.
"He committed to the club. He sees the vision going forward, and he believes in that.
"He knows it won't happen overnight. He has had a brilliant season with 20 goals until now, and hopefully there are many more to come."
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