Claude Puel described the timing of the rumour's surfacing as strange.
Fonte has been linked with a move to Manchester United, with The Times the first to report the news, whilst links have intensified over recent days as the Mirror report that Arsenal have joined the race to sign the Euro 2016 winner.
But the Southampton manager has called into question reports linking his leading defender with a move away from St. Mary's to the North West, citing their emergence just days before the Saints are due to take on the Red Devils in the Premier League.
Puel said, via Sky Sports: "There is no problem with Jose [Fonte] but it is strange that this rumour comes up just before the game that he might go to United.
"But there is no problem with Jose. He is a very good professional and he has trained well this week. It is important to have Jose with us and I hope to have him against United."
Jose Fonte won the European Championships with Portugal earlier this summer
Fonte joined the Saints way back in January 2010 for as little as £1.2 million, at a time when the Saints were languishing in League One.
The Portuguese international has been an ever-present figure at the club throughout their rise back up through the leagues to England's top table, and he is now set to form a key part of the south coast club's defence as they venture into Europe for only the eighth time in their history.
Interested: Manchester United manager Jose Mourinho
However, the Saints captain could well find himself representing compatriot Jose Mourinho's Manchester United in European competition, if reports are to be believed.