The centre half, who is out of contract next year and is currently being pursued by Cardiff, has worn the armband at some stage during all three of Saints’ pre-season friendly matches this summer.
Ronald Koeman confirmed after Monday’s 1-0 win at Swindon that he had not made a final decision on who would be given the role this term, but he hinted that Fonte is the favourite, with Steven Davis – who captains Northern Ireland – as the next option.
The Saints manager also suggested that new contract offers for Fonte and midfielder Jack Cork could be in the pipeline, with both players due to become free agents in a year’s time.
“We know they are important players for us, and the club will do everything to keep all the best players,” he said, when asked if fresh deals were to be handed to them.
It is understood some communication has already taken place over the possibility of extending Fonte’s stay by a further two years.
Saints have already rejected one bid from Cardiff for Fonte, and the Championship club were last week planning another approach.
But, while they have plenty of financial power, it is unlikely they will be able to tempt the St Mary’s board into selling, especially with the likely exit of Dejan Lovren.
Cork is also attracting interest from a number of Premier League clubs, with Leicester the latest to send a scout to watch him, in the win at Swindon.
The 25-year-old again faces significant competition for a regular place in the starting line-up this term, with fellow defensive midfielders Morgan Schneiderlin and Victor Wanyama still in place, while 19-year-old Harrison Reed is emerging as a serious contender ahead of the new season.
On the skipper front, Koeman said that goalkeeper Kelvin Davis will remain as club captain, and that the 37-year-old is the undoubted leader of the group.
But he wishes to continue with the policy of an outfield player being given the armband on matchdays, although he will not publicly confirm his decision on who will be chosen until the start of the Premier League season.
“I am thinking about that, but first of all the captain is Kelvin Davis,” he said. “Kelvin Davis is the captain of the club, he is the captain in the dressing room.
“But I prefer to have the captain in the field, as a player, and that makes that decision that Jose is the captain – maybe Steven Davis, when Jose was not playing – but finally I will make the decision to everybody when we start the season.”