Newcastle signed Isak from Real Sociedad for about £60m in 2022
Alexander Isak wants to explore his options for a move away from Newcastle this summer after missing their pre-season tour of Asia.
The club has selected a 30-man squad, but said the Sweden striker "misses out with a minor thigh injury".
It is understood some of Europe's top clubs have been aware Isak has been looking to take the next step in his career.
A source has told BBC Sport Liverpool are still interested in the 25-year-old, despite signing Eintracht Frankfurt strikerHugo Ekitikefor an initial £69m.
On Saturday Newcastle manager Eddie Howe said Isak would"absolutely" be part of the squadfor the games in Singapore and South Korea.
BBC Sport has contacted Newcastle for comment.
Isak scored 27 goals in 42 appearances in all competitions for Newcastle last season.
He was left out of Saturday's 4-0 defeat at Celtic in the first of their pre-season fixtures.
Newcastle have maintained Isak is not for sale and, speaking at the weekend, Howe said he was "confident" the player will be at the club at the start of the season.
"It's difficult for me to give 100% clarity on any player," Howe said after the Celtic game.
"Alex is happy at Newcastle. He loves the players he plays with, the staff, the team and I've never had any issue with him."
Newcastle had a £70m bid rejected for Ekitike, while they have an interest in Brentford forward Yoane Wissa.
Meanwhile, Newcastle defender Lewis Hall, who has not featured since February with a foot injury, has been included in the tour squad.
Newcastle face Arsenal on Sunday in Singapore before travelling to South Korea to play a K-League All-Star team on 30 July and Tottenham on 3 August.
Newcastle legend Alan Shearer said the claims that Isak's absence from their Asia tour are injury-related are "ridiculous".
The former England striker, who scored a record 206 goals for the Tyneside club, believes they should have been open about the situation.
"It's ridiculous what Newcastle put out this morning to say he wasn't on the trip because of a slight thigh injury," said Shearer.
"If they thought people wouldn't see through that... it was disappointing.
"They should have just told the truth straight away. I understand it's a very difficult situation for them, but it is what it is.
"Eddie Howe has to use all his persuasive powers to do what he can and try to make him stay at least one more year. If that can't happen then it is what it is.
"You have to get the very best deal for the football club and if someone is prepared to pay north of £150m, and if he really, really wants to go, you can't step in his way."
Newcastle have been steadfast in their stance on Isak throughout the summer as Howe looks to keep his squad intact for a return to the Champions League.
The forward has three years left on his contract and the Magpies, owned by Saudi Arabia's Public Investment Fund (PIF), are in a comfortable position with profit and sustainability rules (PSR), meaning they are under no pressure to sell.
Most Premier League clubs are unable to match Newcastle's reported £130m valuation.
Arsenal have previously been credited with an interest and have the budget, but they have since turned their attention to his fellow Swede Viktor Gyokeres and close to finalising a deal.
Manchester City have the funds to go after Isak but are unlikely to pursue a transfer with Erling Haaland under a contract until 2034.
Chelsea have also added strikers Liam Delap and Joao Pedro to their squad this summer.
Premier League champions Liverpool have already spent more than £250m this summer, including Florian Wirtz for a potential British record fee of £116m.
Liverpool's income has been boosted this year thanks to several key factors, led by the £175m they received in prize money for winning the Premier League.
Last season was also the club's first full campaign with an expanded Anfield Road End and therefore a higher capacity.
From 1 August they have a new kit deal with Adidas, which some reports value at £60m per season, more than their existing partnership with Nike.
Those factors, combined with comparatively low transfer spending in previous windows, mean Liverpool find themselves well within the Premier League's profit and sustainability rules (PSR) that limit clubs to losses of £105m over three years.
Liverpool chief executive Billy Hogan has said their investment this summer is the result of long-term planning.
"It doesn't just happen; it's been years in the making,"he told the Athletic.,external
"We also recognise, having won the English league title for the 20th time, that this is one of the biggest clubs in the world. We want to make sure that we are behaving like one.
"Having massive global stars come and play at Anfield, filling out stadiums in Hong Kong and Japan, those are things we expect and want to do."
How can Liverpool afford Isak after spending so much?
We asked for your views after Isak was left out of the squad. Here are some of your comments:
Gary:If these tours are all about driving commercial revenue, surely you take your star striker regardless of a minor injury?
Kevin:Concerning. I hope it is just precaution. It would be really disappointing if he does leave this summer after all the hard work last season to get into the Champions League. Lack of transfers in areas and missing out on targets isn't making me feel any more confident for the coming season either.
Martin:Until he comes out and says he wants to leave, he is injured. Full stop.
Richard:I hope I am wrong but I do not see Isak being in a Newcastle shirt next season. I think the club will sell, but the way transfers have fallen so far, I worry that we will not be able to recruit to the level we need.
Bob:Is "thigh injury" just an excuse and he is on his way out? Be honest - the fans deserve it. If we go into the season with one striker who is not proven we have got no chance.
Kevin F:Isak had thigh problems end of last season so this is nothing new. But if it is true then it should have been sorted out by now. I just hope it's nothing more.
Mark:I think he is unsettled and can see him moving to another club. If he does, we desperately need other players up front. I hope I am wrong.
Richard:Something isn't quite right. What really needs to happen here is Isak to come out and say he is staying and that's it, or we are going to have speculation all the time. Is it his agent fuelling the situation by saying: "Why stay? You could earn mega bucks elsewhere."
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