However, the Reds are yet to struck a deal with any clubs for the out-of-favour pair, nor left-back Alberto Moreno, as Klopp looks to remould his squad.
According to the Mirror, however, there is still considerable interest in both Sakho and Markovic.
Liverpool were previously claimed to value the Serbian at £20 million, but this has since dropped to just £8 million.
Moves for Bruno Martins Indi, Joel Veltman and Kurt Zouma have proved fruitless, while Kenny Tete has joined Lyon, ensuring both Sakho and Calum Chambers remain on the Eagles’ radar.
However, Liverpool won’t allow the Frenchman to leave on loan, insisting on a permanent deal, with the price tag standing at £30 million.
There are likely many more to follow them through the Anfield exit, as work continues in earnest this transfer window.
The Reds are waiting for assurances from the Saints that they would be willing to negotiate for Van Dijk, while reports on Monday night claimed a new £74.2 million bid has been made for Keita.
While deals for Klopp’s priority targets are proving increasingly protracted, the same can be said of the club’s potential outgoings.
Shifting deadwood such as Sakho, Markovic and Moreno is still a key focus for the transfer window, as they are highly unlikely to be given any opportunities if they remain on Merseyside.