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.
This 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 £40million 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]."
Rodgers also confirmed the club was working on strengthening the squad further ahead of a season-opener against Stoke on August 17.
With Suarez absent from the travelling squad, striker Daniel Sturridge was a notable inclusion having recently returned to full training following an ankle injury.
Boston Red Sox and Liverpool owner Henry on Friday stressed that Suarez will have to stay with Liverpool and join their push for a top-four finish next season.
Liverpool's target is the elite level of European football, and captain Steven Gerrard has said recently that Suarez holds the key to how the club will perform in the new campaign.
Henry knows the significance of Champions League football which, as well as offering the prospect of challenging for a trophy Liverpool have won five times, also offers huge financial benefits.
Henry said: "I think for all of the top clubs it's extremely important. Especially for Liverpool, since we have not been in Europe and are not in Europe this year - and we haven't been in the Champions League for a while - obviously to sell Luis to a rival for one of those positions would be ludicrous.
"I have told (Arsenal chief executive) Ivan Gazidis that Luis is not for sale. I am unequivocal on that."
Denmark international defender Daniel Agger was appointed Liverpool's new vice-captain on Friday.
The 28-year-old replaces the retired Jamie Carragher as deputy to Steven Gerrard after making 209 appearances for Liverpool since joining from Brondby in 2006.
Rodgers told LFC TV: "The job of the captain and vice-captain here at Liverpool is very, very important. I wanted to give myself time over the course of the pre-season to assess a number of the players and obviously Daniel was one of them.
"His loyalty and his passion for Liverpool is second to none. And if you add that on to his footballing qualities, then I think it's a good choice for everybody."