Liverpool captain Steven Gerrard believes a top-four finish is possible if they can iron out their consistency issues but whether striker Luis Suarez is around to spearhead that challenge remains in doubt.
Press Association Sport understands the club turned down a £30million bid for the Uruguay international from Arsenal last week.
With the spectre of Real Madrid - who Suarez admitted would be difficult to turn down - loitering in the background it seems the 26-year-old is destined to be in the headlines for most of the summer.
While Liverpool insist the player is not for sale his public pronouncements on his dislike of his treatment by the English media and apparent interest in Real have made things difficult for the Merseysiders.
But they are not prepared to be backed into a corner in terms of selling the player who was the Premier League's second-highest scorer last season - especially in the face of offers like Arsenal's which was well below what the Reds consider to be Suarez's true value.
While the Suarez saga seems set to play out for several weeks - the striker is on extended leave after international duty and not expected back until the Australian and Thailand legs of the club's pre-season tour - most of the squad are well into their pre-season training and Gerrard is optimistic bigger strides can be in the coming campaign.
The Reds finished seventh in May but lost just one of their last 12 league matches.
However, a poor start - they did not register a Premier League win until September 29 - and then subsequent fluctuating results affected their chances of regaining Champions League football.
"The final five or six months of the season were fantastic, we showed fantastic form - I think it was top-four form," said the Liverpool captain.
"We certainly finished the season really strong but we were very inconsistent from August to Christmas - that's the reason why we never managed to achieve what we set out to do, which was a top-four finish.
"But I felt at times in the season we played some brilliant football.
"If we can find that level on a consistent basis, I've got confidence we can break into the top four.
"The realistic message is to say to the fans that the last four or five months of the season were really positive, we played well.
"If these (new) signings are positive and successes they can add to those performances.
"If the fans get behind us and show the support that we know they can, I believe we can push into the top four.
"That would be a fantastic achievement if you look at the standard of the teams in this league."
This year the fixture list has been slightly kinder to Brendan Rodgers, embarking on his second season in charge.
In their opening nine league matches they face only one team who finished above them last season.
"It could have been an awful lot trickier," Gerrard told LFC TV.
"We've got to be reasonably pleased with the start we've got but you need to turn up and perform.
"I look at the fixtures all the time but the most important thing is to not get too carried away and look at that first game (against Stoke).
"We need to get off to a good start in terms of being positive for that first home game."
The arrivals of Sunderland goalkeeper Simon Mignolet, Manchester City defender Kolo Toure, Celta Vigo forward Iago Aspas and Sevilla midfielder Luis Alberto have provided a welcome boost.
More signings are expected but it appears the club will have to forget about a deal for Shakhtar Donetsk midfielder Henrikh Mkhitaryan as although they were willing to pay the club's £20million asking price they never had chance to speak to the player and he seems Borussia Dortmund-bound.
But now Rodgers has been able to properly instil his methods at Anfield Gerrard hopes it will start providing results from the off.
"When you get a new manager and new staff it takes a while for the message to come across and for all the players to take it on board," he added.
"But we've also got to be men about it and take responsibility that, at times, we didn't turn up and perform.
"We have to make sure those mistakes and performances don't happen next year and, if they don't, hopefully we can have a good season."