It's up to them to decide which way it goes.
In those three, sporadic, deals, Liverpool have been the selling party twice.
But regardless of Valverde's preferences, there's also a need to shift money from the wage bill.
Liverpool appear to be keeping their transfer business very close to their chest since last summer's debacle with Van Dijk, but the names they are being linked with should allow fans to feel excited.
The 25-year-old Brazil international, who watched his new side's 3-0 win over Levante on Sunday, will perform a ceremonial signing of his contract at 1130GMT on Monday before a photo shoot on the pitch and a press conference.
They'll have to act quickly though with Liverpool interested as well.
Goal's South American expert Daniel Edwards has described how the man who can't stop dancing, Yerry Mina, is no slouch on the pitch and an able successor for Javier Mascherano.
Is there a middle ground for Klopp?
In 2015, when Sergio Aguero's jersey number changed post the exit of Edin Dzeko, Aguero himself offered to sign and send back the outdated shirts.
"The difference is that there has been a substantial reduction in the cost of this transfer".
Firmino still has two years to run on his current deal but is set to be rewarded for his prolific form this season. Maybe a goalkeeper, to finally replace the ever-unconvincing Simon Mignolet? He was gutted in the summer that RB Leipzig delayed the transfer for a year.
The Brazilian is reportedly poised to join Inter through the rest of the season, with the Serie A side hoping to secure an option to buy that's below €20 million.