The 32-year-old, who helped Portugal to their summer triumph at Euro 2016, has 18 months remaining on his current contract at St Mary’s.
Fonte was linked with a move to Old Trafford in the summer and Jose Mourinho is reportedly interested in making a move in January to bolster his injury-hit defence which will also be without Eric Bailly due to his Ivory Coast commitments at the African Cup of Nations.
The Southampton captain revealed earlier this week that he had been offered a pay rise in the summer, after his Euro 2016 victory, but that the club were unwilling to extend the length of his contract.
As a result, Fonte took to social media to clarify his current situation at the club.
"Just to set the record straight I did not reject a new contract," he said on his Instagram page. "In fact I have been informed by Southampton that they are not offering me a new contract.
"My focus is on Thursday [against Hapoel Be'er Sheva in the Europa League] helping us win the game."
He said in an interview earlier this week: "There's no contract on the table. There was in the summer, they offered me a pay rise. They didn't offer me a new contract.
"They offered me a pay rise which I'm entitled to discuss with my agent and entitled to say no to as well. I'm entitled to have my own opinion, so apart from that that's it."
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