The Saints captain has "formally asked for a transfer", according to Southampton director of football Les Reed.
Fonte previously claimed that he had not been offered a new contract by the club, with 18 months left to run on his current deal, but Reed said that this was not the case.
"He's had several opportunities to improve the contract situation. He's reserved his right not to do that," Reed told BBC Radio Solent.
"He's made it very clear he would like to explore the opportunities for a transfer.
"That's where we are at the moment, Jose wants to leave the club. He's formally asked for a transfer".
Both Manchester United and Everton have been rumoured to be interested in Fonte and interest is likely to intensify after the Portugal international's transfer request.