Suarez was handed an eight-game suspension and a £40,000 fine in December after being found guilty of racially abusing Manchester United defender Patrice Evra in a Premier League match at Anfield.
The controversy was reignited in February when Suarez seemingly refused Evra’s handshake as the teams conducted their traditional pre-match greeting in the return meeting at Old Trafford.
Suarez then reopened old wounds during an interview with a Uruguayan television show last month, where he accused United of having too much power and blamed Evra for the failure to shake hands.
The striker was jeered and booed by the crowd during Uruguay’s Olympic Games defeat against Great Britain at the Millennium Stadium this week, but Rodgers has noted that rival fans only single out good players for criticism.
“Luis probably still feels a little bit of injustice about last season, but for me the message is that we have to move on.
Brendan Rodgers on Luis Suarez
“The first point is that opposition fans only give people stick because they’re good players – you don’t see bad ones getting it,” Rodgers said.
Rodgers continued: “Luis probably still feels a little bit of injustice about last season, but for me the message is that we have to move on.
“We have to move forward. What’s happened has happened and let’s let it go now, however hard it is. We want to be winning games and doing our best for the football club.”
Suarez saw his participation in the Olympics come to an end with the loss to Team GB as the highly-fancied Uruguayans were dumped out.
Rodgers is now looking forward to welcoming the 25-year-old back into the fold with the Reds’ season having already begun with Thursday’s 1-0 victory over Belarus’ FC Gomel in the first leg of their Europa League third qualifying round clash.
“It will be fantastic to have Luis coming back, and he is already fighting fit,” said Rodgers, who replaced Kenny Dalglish in the Liverpool hotseat this summer.
“He will have a couple of days off and join up with us after the weekend. He’s been playing games, so he will already be up to a decent level of fitness, maybe even higher really, because he’s had more competitive games. I’m really looking forward to working with him.”
Rodgers is looking to strengthen his squad further ahead of the start of the new season but knows he will have to remain patient.
He said: “There is nothing imminent just yet, not that I am aware of, but hopefully things will progress over the next couple of days. It may take one or two moves to spark everything off.
“I want players in sooner rather than later, it is important to get the group together as quickly as possible, but if not we will just have to be patient.
“I have also looked at one or two loan deals from abroad. There are some quality players in that market that I have enquired about. The make-up of the group will change before the season starts and that will change the dynamic of the team also.”