The Reds cannot win any silverware this season and they are nine points adrift of the top four.
An extended absence from Europe's elite competition - Liverpool have not played in the Champions League since 2009-10 - causes further issues in relation to the recruitment and retention of players.
Striker Luis Suarez, the top-flight's leading scorer with 22, has given an interview in his native Uruguay in which he reportedly said if another club with better European prospects came calling he would talk to them.
That seems at odds with his continued insistence he is happy on Merseyside, but even though Juventus have been linked with a summer bid, Liverpool privately are confident of holding on to the 26-year-old, who signed an improved contract at the beginning of the season.
If Agger's prediction is right then Suarez's ambitions could be fulfilled at Anfield.
"It is a club that will have trophies, I think it goes without saying," said the centre-back.
"I believe it will come, of course. It will not be this year, because we are changing the style of play as we have not got the results we would have wanted but we have played well.
"There have been a few worries and it has something to do with stability and we must also have a bigger squad.
"These are the things we need to work towards next season.
"If we can keep the same level in more matches than we do this year it will look better for next season."
Agger credited Rodgers with having a positive impact on his fitness, which has allowed him to have his best run in the side.
The 28-year-old has started 29 of Liverpool's 30 Premier League matches, missing one only because of suspension.
Agger has made just four other appearances in the Europa League as Rodgers has sought to manage the defender both on and off the pitch.
"For me it's about being fit and I've been the fittest in years," the Denmark captain, preparing for World Cup qualifiers against Czech Republic and Bulgaria, told Danish website sporten.dk.
"I have not missed a game because of an injury and I think that is the first time in my career.
"Brendan Rodgers is undoubtedly the reason I have played all the matches without injuries this year and I cannot be anything but pleased.
"I must give the new coaching team great credit for it, but especially the new manager gets the greatest credit for this.
"It is not I who can take these decisions, it is he who has decided to adjust my training specifically for me.
"The new coaching team have come up with a form of exercise taking into account the individual, and it is something I have needed.
"My training volume is scaled down and then I have an increased recovery period."
The same approach has allowed Liverpool captain Steven Gerrard, 33 in May, to play every minute of Premier League action this season.
It could not help midfielder Joe Allen, however, whose season has been prematurely ended after it was decided to send him for surgery on a troublesome shoulder injury.
The 23-year-old withdrew from the Wales squad on Sunday because of the long-standing issue with his left shoulder and the club then decided to bring forward plans for an operation.
Allen, who has had surgery on the injury before, has had the problem for some time but it began to get worse in October and has got to the point where corrective intervention is required.
"Joe Allen is due to have a left shoulder operation tomorrow morning in Liverpool and will be ready to return to football at the beginning of next season," first team doctor Zaf Iqbal told Liverpool's website.