Saints have lost many of their key men this summer and reports had suggested that Fonte could also be on his way out of St Mary's, with Cardiff City and Hull City both thought to be keen.
However, the centre-back is ready to pledge his future to the club by signing an extension to his current contract, which runs out next year.
"I am in negotiations to renew my contract. There have been offers from other clubs but I feel happy at Southampton," said Fonte in the Daily Mirror.
Fonte concedes that it will be difficult for Southampton to overcome the departures of Luke Shaw, Rickie Lambert, Adam Lallana, Calum Chambers and Dejan Lovren.
However, new boss Ronald Koeman has already brought in some reinforcements and Fonte is expecting further business to be done.
The 30-year-old said: "Ronald Koeman already knew he was going to lose some players. Of course, he can't be very happy with the situation but he has already signed three quality players.
"Ryan Bertrand came in to Luke Shaw's place and has done good work, Graziano Pelle scored a lot of goals last year in Holland and Dusan Tadic has a lot of technical quality.
"We still need another three or four more. The players who have arrived have brought competitiveness."
Fonte added: "I'm sad that so many players have left, but that's football."