The Argentine has just one year left on his contract with the Saints and the bookmakers make him odds on favourite for the job with no better than 1/3 available.
After Southampton's final game of the season against Manchester United, Pochettino said it might be time for the club to embark on a "new project."
"I have said that this club now deserves to be in a new project, the board has to decide how that happens, two years, three years or four years - I just want to sit down and talk and we will see what happens," he said.
Pochettino guided Saints to an eighth-place finish in the Premier League this term and earned positive reviews for bringing an entertaining style to a young fresh team.
However, the team risks losing a number of their stars in the summer with Adam Lallana, Luke Shaw and Dejan Lovren all heavily linked with moves away from the club.
Tottenham are without a manager after sacking Tim Sherwood at the end of the season.
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