Brendan Rodgers' reign of just over three years came to an end on Sunday afternoon when he was sacked following the Reds' 1-1 draw in the Merseyside derby - with that decision taken on the back of a string of poor performances and indifferent results.
Reports, such as those from Sky Sports, are suggesting that former Borussia Dortmund boss Jurgen Klopp is the frontrunner to succeed Rodgers and could be in place by the end of the week, with a view to taking charge of his first game away to Tottenham Hotspur a week on Saturday - the first fixture that follows the international break.
Aldridge wrote in his Liverpool Echo column that tightening up the side's leaky defence has to be a priority going forward.
"We need to be strong, more rigid, more mean and keep more clean sheets. I don't think I can state strongly enough that you have to keep clean sheets.
"We panic far too easily in defence and that will always give the opposition a chance.
"That'll be down to whichever system the new boss employs because we he'll have to work with the same group of players until January at the earliest.
"Obviously, we have some good players going forward. Daniel Sturridge, Christian Benteke and Danny Ings are all good strikers, so we are potent up top.
"We just need to make sure they get proper service.
"But if you can't keep clean sheets then you are eventually going to find it difficult to win games."
It has been a trait of Liverpool over the past three seasons that they have conceded too many goals, so of course it will be a part of the team that the new manager will look to get to work as soon as he is appointed, but there is also the issue of solving Liverpool's problems in front of goal to contend with.
They have only managed to find the net more than once on one occasion this season, and since April they have only scored more than once in three games in total.
When you look at the strikers they have in their ranks in Daniel Sturridge, Danny Ings and Christian Benteke, all three have shown they are capable of getting their fair share of goals for a side in the Premier League during the course of the season - so there's an evident pool of talent there.
It will just be a question of how you get the best out of them. But whoever is Liverpool manager still has an opportunity if he manages to hit the ground running of engineering a pretty successful season.
The club are still in the League Cup, can qualify from their Europa League group and are currently six points away from the top of the Premier League, which is hard to believe given their performances of late, so to write off their chances of finishing in the Champions League places is a little premature.