Ravel Morrison has returned to parent club West Ham from Cardiff City on compassionate leave.
Brighton boss Sami Hyypia is weighing up a move for former France captain Alou Diarra.
The Uruguay international is enjoying an outstanding season having scored 20 goals for the Anfield outfit.
That has led to speculation that other clubs could move in for the £40million-rated forward if the Reds' absence from the 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 is confident Suarez shares his vision for the club and 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."
Suarez signed a long-term contract at Anfield in August.
Rodgers is determined to keep firing on all fronts.
He said: "When you are a club like this you are judged on your trophies, and we want to improve in the league as well."