Tim Sherwood is expected to be relieved from his 18-month Lillywhites contract at the end of the season following a number of heavy defeats.
Netherlands boss Louis van Gaal has been heavily touted to replace Sherwood after the World Cup, and has admitted that he would like to test himself in the Premier League in the next phase of his career.
Dutch legend Ruud Gullit has claimed that Van Gaal to White Hart Lane is "a done deal", but The Telegraph reports that Spurs are very impressed with the work done by Pochettino at St Mary's Stadium.
The Spaniard has taken Southampton from relegation candidates to European hopefuls since being plucked from La Liga to succeed the popular Nigel Adkins only 15 months ago.
It is believed that he has several fans within the board room at Tottenham, who favour his willingness to work with a director of football as he has done alongside Paul Mitchell at the Saints.