The Brazil international's £142m (€160m) move to the Nou Camp has triggered a frenzy of activity in the January transfer window, with the Reds linked with a host of players.
Monaco's Thomas Lemar, Leicester City's Riyad Mahrez and Roma midfielder Kevin Strootman have all been paired with moves to Liverpool.
Attempts to lure Naby Keita from RB Leipzig ahead of his scheduled arrival in the summer have also been mooted, though the Bundesliga club are unwilling to negotiate an early release.
The need to recruit additional cover in midfield could be accentuated by the departure of Emre Can, who is destined to leave Anfield with his contract due to run out at the end of the campaign.
And with captain Jordan Henderson having missed the last four games due to a hamstring injury Danny Murphy believes fresh blood might be required in that position.
"In the middle of the park, there is a gaping hole in midfield," he told Sky Sports, according to Sport Review. "He [Klopp] is letting Emre Can go at the end of the season.
"Liverpool need a powerful presence and a creator. There is always a leader, someone you can hang your hat on at Liverpool."
But Phil Thompson wants a much-derided defence further improved with another centre-back and a goalkeeper. However, he does not expect either player to arrive in January.
"I've said all along the defence is the important area which needs addressing," he told Sky Sports, per The Sport Review.
"I don't think Van Dijk will solve it on his own so another centre-back, who is a real leader, and a top-class goalkeeper are required, but I don't think they will happen in January as it has to be the right players."
Former Liverpool managing director Christian Purslow also feels the club need to add further competition for Simon Mignolet and Loris Karius between the sticks, with both players having been continually rotated this season.
"The obvious need is for a world-class goalkeeper," he said, according to Sky Sports, report The Sport Review. "If there is one thing I'd like the [Coutinho] money to go on, it would be a world-class goalkeeper."