The Uruguay international was not named in a 22-man squad to play Celtic in a pre-season friendly in Dublin on Saturday and he is training on his own after Rodgers took exception to his public pleas to leave Anfield in search of Champions League football.
Friday morning saw Liverpool owner John W Henry insist the 26-year-old will not be sold and say it would be "ludicrous" to let him join domestic rivals Arsenal, who have had an offer of £40 million plus £1 rejected.
At a press conference in Dublin, Rodgers said: "Luis is training on his own and he understands totally where we're coming from.
"It's been a difficult period for him but it's my job to protect the group. Once he's back with the spirit he'll rejoin the group.
"We're quite calm. The club is in control of the situation. We've got no inclination to sell and we've been strong on that.
"Luis has fought for his life for Liverpool. There will come a point where he'll recognise the club is not going to sell and then he goes on to the pitch and he'll give 100 per cent.
"He's a world-class striker. I've got no question that when he's back he'll have a similar impact [to last season]."