Karius' two costly errors in the Champions League final last month have shown the need for a world class stopper at Anfield if the club is to kick on and establish itself back among the Premier League and European elite on a consistent basis.
Roma's Alisson has been heavily linked, while AC Milan teenager Gianluigi Donnarumma has also been mentioned as an option since Karius' disastrous night in Kyiv. Even an offer to keep Gianluigi Buffon out of retirement has been rumoured.
But Don Balon claim that a Liverpool offer for Oblak totalling €90m (£79m) has already been made. That is short of the €100m that Atletico apparently want, but is the best proposal so far.
Liverpool are already responsible for making Virgil van Dijk the most expensive defender in the world following his January move from Southampton and will raise the bar for goalkeepers beyond Gianluigi Buffon's historic 2001 move to Juventus should this story comes to fruition.
Liverpool were always set to buy a new goalkeeper this summer, but since the Champions League final the goalposts have moved.
Previously, a new second choice to replace Simon Mignolet, who is determined to land a starting job elsewhere, would have sufficed. But given Karius' shortcomings on the biggest stage, the club have had to set their sights much higher.
Whether Karius stays as second choice remains to be seen but is certainly the likely option.