However the 25-year old penned a new long-term deal with the Anfield club earlier this week after returning from Olympic duty to bring an end to speculation surrounding his future.
Despite having four years remaining on his first Liverpool contract, Suarez has now tripled his wages to be one of the club's top earners on around 127,000 pounds per week.
"There was genuine interest from other clubs," Rodgers told Sky Sports. "I had only just come through the door when a fax came through about him.
"It is brilliant that someone of that quality has agreed to stay with the club. It is great for the Premier League. It is a new beginning for him. There are very few world class strikers around. He is a very important signing for the club. He is still young and has his best years ahead of him."
Liverpool begins the Premier League campaign on Aug. 18 away to West Bromwich Albion.
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