Four new faces have arrived and Klopp wants at least another two. Who should be his priority?
Sadio Mane was the latest player to join as he completed his signing from Southampton yesterday. Marko Grujic finally links up with the Reds with a deal having been in place since January, along with Joel Matip and Loris Karius.
It is hard to think that Liverpool's business is complete as there have been numerous other names that have been linked with a summer move to Anfield, in particular in two positions: left-back and central midfield.
Liverpool have had a bid rejected for Leicester City left-back Ben Chilwell, and according to the Liverpool Echo, they are not prepared to pay the £10 million asking price that has been slapped on him by the Premier League champions.
A midfielder who can operate centrally also seems to be on the radar of the Reds with a bid for Udinese's Piotr Zielinski while Borussia Monchengladbach's Mahmoud Dahoud has also attracted the attention of the Reds, but which need is more urgent? The Echo reported a bid for Zielinski, while interest in Dahoud has been reported in several outlets including The Guardian.
Judging by the pursuit of a left-back, Klopp looks as if he will keep hold of Alberto Moreno in some capacity despite some of the Spaniard's downsides - which featured in a disastrous performance in the second half of the Europa League final back in May against Sevilla. Ben Chilwell and Andrew Robertson are not exactly accustomed at the highest level - with the former very inexperienced although highly rated - with all the signs pointing to competition for Moreno in that area of the field rather than an outright replacement.
An impressive pre-season from Brad Smith could put the pressure on that position and make the central midfield area that little more pressing to address.
One could say that Liverpool are pretty well stocked in the central midfield area. Emre Can looks as though he could be the mainstay for many years to come, while Jordan Henderson, Lucas Leiva, James Milner and Joe Allen all play the role.
Klopp may not want to use Milner in a central role, however, Allen is attracting interest from elsewhere and Lucas has admitted his future at the club is uncertain.
The Brazilian, however, could be used as a centre-back if he were to remain at the club after filling in the position many times during the second half of the season, including in the League Cup final against Manchester City.
The Reds boss has often opted for a central midfield two, and given that Henderson is heading into pre-season on the back of a campaign where injuries took their toll, it would be wise for the midfield area of the side to be addressed first if it at all possible.
Klopp seems intent on getting everybody in place before the start of the first pre-season game in nine days time so he can hit the ground running and that area is one where more bodies are needed.