Fonte attracted serious interest from Manchester United over the summer.
The Mirror says the Saints are desperate to keep Fonte on the south coast and are already in discussions over a new £70,000-a-week deal for their influential captain.
But the 32-year-old appears to be in no rush to put pen to paper on fresh terms at St Mary's, saying: “There's nothing on the table, so I'm waiting.
"I'll see what happens. I'm just focusing on performing and we'll see what happens.
“We haven't agreed anything, it's just talks."