The club captain had been linked with Manchester United over the summer.
On social media yesterday, Fonte's statement read: "Once in the national team only national team interviews/talks are allowed hence my 'let's leave that for another time' when asked about questions regarding my own club situation.
"To make it perfectly clear to everyone that might have some difficulty understanding I am a Southampton player, and proudly have been since 2010, understand that once I step on the pitch with the Saints shirt and armband I give my blood, sweat and tears for the club and will always will no matter what you read or think.
"My professionalism means everything to me, and no one can point me a finger about it. I am fully committed to succeed with my two teams @southamptonfc and @selecoesportugal.
"Thank you #wemarchon."