Liverpool are yet to make a formal bid for Isak, who could command a deal worth around £120 million, according to The Athletic.
The Reds have communicated their interest in the 25-year-old to Newcastle, whose stance is that he's not for sale.
The Magpies are believed to be pushing to get a deal for Hugo Ekitike, worth around £61 million, over the line.
It's unclear if the Eintracht Frankfurt forward is seen as a potential replacement for Isak or if the plan would be to play them together.
The Frenchman has also been linked with a transfer to Liverpool in recent weeks.
It has been suggested that the Reds could use the supposed situation as leverage - that is, they start talks for Isak or enter the race to sign Ekitike.
Liverpool are aiming to add a striker to their squad this summer, following the high-profile arrivals of Florian Wirtz, Jeremie Frimpong and Milos Kerkez.
Luis Diaz has been linked with a move away from Anfield, with Bayern Munich and Barcelona said to be interested, which could help to pave the way for another big-money deal.