Liverpool target Alexander Isak training at Real Sociedad

Alexander Isak is working on recovering from injury at Real Sociedad's training ground, the LaLiga club has confirmed, after missing Newcastle's preseason tour amid growing speculation over a move to Liverpool.

Newcastle have cited a "minor thigh injury" as the reason behind Isak'  absence from the team's tour of Asia.

 He missed Sunday's game against Arsenal in Singapore and a match against a K-League XI. He will also not feature against Tottenham Hotspur in South Korea this week.

A Real Sociedad spokesperson confirmed on Thursday that Isak has been working on his recovery at their training ground, Zubieta, outside San Sebastián this week.

Isak played for La Real for three years, becoming one of Europe's most in-demand young forwards, before joining Newcastle in 2022.

Newcastle are reluctant to allow Isak -- who has scored 44 Premier League goals in three seasons on Tyneside, and has three years left on his contract -- to leave, with coach Eddie Howe insisting earlier this month that the player is "happy" at the club while admitting that "you never know what can happen."

Liverpool have already beaten Newcastle to the signing of Hugo Ekitike from Eintracht Frankfurt this summer in a deal worth an initial £69 million ($91m). 

The Premier League champions have already added Florian Wirtz, Jeremie Frimpong and Milos Kerkez to the squad, but allowed another forward, Luis Díaz, to join Bayern Munich this week.

"[Isak] is still our player. He's contracted to us," Howe said this week. "We, to a degree, control what is next for him. I would love to believe all possibilities are still available to us. My wish is that he stays, but that's not in my full control.

"We have not received a formal offer for Alex, from any club."