As reported in The Argus Brighton have rejected a huge £8 million bid from Napoli for the Scotland midfielder who has impressed since signing for the club from Chelsea.
It is said that the club value Gilmour as more valuable than the initial bid after Brighton paid £9M for the midfielder in 2022.
Gilmour is currently with the squad in Tokyo as they prepare to face Japanese sides Kashima Antlers and Tokyo Verdy on their preseason tour.
Many fans believe the side should do everything they can to keep the player but that may be tough as Napoli is a huge chance for Gilmour to shine and possibly lift some silverware early on in his career.
£8M is a very low price for what is an established player especially in the modern market and Napoli will likely have to double their offer if they want a chance to sign the English playmaker.