The Ulsterman admits he would be sympathetic towards his star striker if the Uruguayan decided to quit the Premier League following his "harsh" 10-match ban for biting Ivanovic
The Uruguayan striker has accepted a three-match suspension for violent conduct and has until 12pm on Friday to lodge an appeal against the additional seven-match punishment.
Rodgers believes the outcry from the incident has been a key factor in the harshness of the ban, with Prime Minister David Cameron even intervening to suggest that the FA should make an example of Suarez.
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"I know at this moment he's visibly very disappointed. I look in his face and for the first time since I arrived here I see a guy – a genuine guy – who is bitterly disappointed.
"It was something he knows was clear, he knows what he did and he expected punishment, but he hoped he would be supported in a rehab process that allows him not to do it again.
"So it will take time for him to come to terms and understand why he's been punished in this way.
"That will make you think, no question. But in a couple of days' time when he is more reflective – because there’s a shock and anger at the moment – a sense of reality will set in.
"Once he feels he knows the support he has from the management and the club it will make him think differently."
Despite Rodgers’ concerns former Liverpool ace Dirk Kuyt, now playing for Turkish side Fenerbahce, isn't worried that his ex-team-mate will quit England.
The Netherlands international exclusively told Goal.com he believes the support Suarez will receive from the club will suppress any thoughts he may have of leaving.
Suarez is seen as the foundation on which Liverpool are hoping to continue to build on next season and Rodgers thinks it’s vital that the club help him at this time.
"For us now it's a case of supporting him, He's part of the Liverpool family and very much part of the future," Rodgers added.
"Even though he’s not playing, he’s very important for us going forward in order for us to succeed.
"We will plan with Luis being here. There is no other thought in my mind – Luis is very much a player I believe will be here."