It had been suggested that Fonte could be among the names to depart Southampton during the exodus of 2014, but the Portuguese defender has confirmed that won't be the case.
Fonte, 30, had been linked with a summer switch that would see him leave St. Mary's and move to the Cardiff City Stadium as the Bluebirds aim to return to the Premier League at the first time of asking.
Earlier in the summer, the centre-half, who joined Southampton in 2010 was linked with a move to Hull City.
It had been reported that Fonte would be offered a wage rise as an incentive for him to join the South Wales club.
"I am in negotiations to renew my contract. There have been offers from other clubs but I feel happy at Southampton."
Koeman has lost five high-profile members of his first team squad, and Fonte has voiced his disappointment about the number of departures that have occurred this summer.
The former Feyenoord boss has added Ryan Bertrand, Saphir Taïder, Dušan Tadić and Graziano Pellè to his ranks ahead of the new season, with a deal for Fraser Forster due to be completed in the coming days.
Throughout pre-season, Fonte has captained Southampton on numerous occasions, only ever losing the armband when he was not on the pitch, to Northern Ireland captain Steven Davis.
Koeman has highlighted Fonte's importance in the dressing room and said that the Sporting Lisbon youth product was one of the first players he talked to following his arrival.
A new central defender is expected to join the club before the close of the window, but Fonte is widely expected to retain his first team spot and lead the Koeman era at St. Mary's Stadium this season.
Southampton play their first home game of pre-season when they host Bayer Leverkusen at St. Mary's this Saturday.