Scotland player Billy Gilmour was offered £8 million by Italian team Napoli, but Brighton rejected the offer.
According to sources, Napoli will likely make another attempt since they think they can pull off a move, even if they saw this offer as only a first.
The Seagulls’ two-match visit in Japan began with the midfielder from Scotland boarding a plane.
They want to capitalize on the success of Japan international Kaoru Mitoma, who has left a lasting effect on the team, by playing Kashima Antlers on July 24 and Tokyo Verde on July 28.
Gilmour participated in 41 games in all competitions last season, starting 24 games in the Premier League.
He still has two years left on his Brighton deal, having joined for £7.5 million in 2022.
Antonio Conte, the manager of Napoli, formerly of Chelsea, won the title in 2023 for the first time in thirty-three years. Napoli finished 10th the previous season.
Brighton is getting closer to acquiring Diego Gomez, a Paraguay international, from Major League Soccer team Inter Miami.
Gomez won’t be able to hook up with Brighton until after the competition since he will be a member of his nation’s Olympic team later this month.
However, sources say talks over a deal are close to completion, with suggestions a fee will be about $18m (£13.9m).