However the 25-year old penned a new improved 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 per week.
Rodgers also spoke of the interest in Suarez that surfaced almost immediately after his appointment as manager of the Merseyside outfit.
"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 begin their Premier League campaign on August 18 away to West Bromwich Albion.