Isak has spoken with the club hierarchy and informed them of his decision, according to Daily Mail chief football reporter Craig Hope.
Liverpool have been the frontrunners for the striker's signature over the summer, taking over from Arsenal, who are now close to completing a move for Isak's compatriot, Viktor Gyokeres.
The Reds are said to be willing to part with the Magpies' £120 million asking price, though they are also facing competition from Saudi Arabian club Al Hilal.
The news comes hours after the announcement made on the Newcastle website that Isak will not travel with the club to Singapore and South Korea, with a minor thigh injury given as the reason for his absence.
That was in direct contrast with manager Eddie Howe's statement at the weekend, when he claimed the Swede would "absolutely" be travelling to Asia. Howe was speaking after Isak played no part in Newcastle's 4-0 friendly loss to Celtic, while the forward has been training alone in recent days.
Those revelations fuelled speculation that the 25-year-old is close to sealing a transfer away from St James' Park, but for the first time, today's news has confirmed that Isak is pushing for a move.
Newcastle will be doing without the services of their 2024/25 top scorer in Asia, where they will face Arsenal in Singapore, before heading to South Korea to play a K-League All-Star team and Tottenham Hotspur.
