Suarez is a fan favourite at Anfield but is widely booed around other grounds across the country, and was given a negative reception at every Olympic venue he played in.
However, Rodgers believes that the Uruguay international could still win the away fans over, citing former England captain David Beckham as an example of how opinions can be changed.
"I didn't hear the reaction [during the Olympics] but top players get a bit of stick at every away ground. But if there is a negative reaction towards a player it is normally because they are good," said Rodgers.
"We have seen it over time and players can become stronger for sure. Looking at the David Beckham scenario a number of years ago, they were burning effigies of him. Now he is king of the world.
"That is how it can change. The most important thing is to recognise where you are at and then move forward."
Suarez recently committed his future to the club by signing a new long-term contract.