The Argentinian succeeded Nigel Adkins in January 2013 and, after ensuring the Saints stayed in the Premier League last term, he has guided them through a season where they have become a permanent fixture in the top half of the table.
However, there have been rumours over Pochettino's future following the departure of the club's chief executive Nicola Cortese in January, with Marseille, Monaco and Getafe reportedly showing an interest in recruiting the former international defender.
But Fonte is keen for a new deal for Pochettino to be finalised following the progress made at St Mary's.
"I think it's massive," the Portuguese defender said. "It's one of the main things. We players love to play under him, we love his philosophy, his style of play, and the way he manages is top.
"He is definitely one of the best managers that I have played under.
"So we look forward to him signing a big, long contract so we can relax and enjoy our time with him."