Arsenal opened discussions over a deal to sign Schneiderlin last week but north London rivals Spurs are also in talks to sign the 24-year-old and believe they are favourites for his signature.
The £18 (€22.7) million-rated France international is emerging as Tottenham's leading target for the summer transfer window as Pochettino looks to improve his squad ahead of the new season and the clubs have been in discussions for several weeks.
Pochettino left the Saints to become Tottenham’s new head coach in May and the pair’s close relationship is key to the deal for Schneiderlin, who has three years remaining on his contract but has told Southampton he wants to leave.
Schneiderlin has spoken glowingly of his improvement under Pochettino and believes re-uniting with the Argentine would be a better career move than moving to Arsenal.
"I think a manager like that is good for every club," Schneiderlin told Goal. "With the quality Tottenham have, Mauricio Pochettino will get the best out of each player.
"He came in and made Southampton play and now Tottenham have a great future.
"He improved me very much. He improved the whole squad and improved me as a player. He's a great coach and good man and it's a shame Southampton lost him."
Tottenham expect to free up room in the squad for Schneiderlin by selling either Etienne Capoue or Sandro.
Capoue has struggled to settle since arriving for €11m last summer from Toulouse, while Sandro has been a target for Napoli but the clubs have been some way apart in their valuation of the Brazilian midfielder.
Spurs are set to announce Ben Davies as their first signing of the summer after the Swansea left-back completed a medical ahead of a £10m switch, with Gyfli Sigurdsson set to move to the Welsh club.
The north London club are also in talks to sign Swansea goalkeeper Michel Vorm as back-up to Hugo Lloris but have dropped their interest in striker Wilfried Bony.
Bony and Chelsea striker Romelu Lukaku are admired at White Hart Lane but a lack of interest in Roberto Soldado means the club are unlikely to spend €25m-plus on a new striker.
Tottenham spent €140m on new signings last season, when Gareth Bale left for a world record €100m, and Pochettino does not expect the club to make many signings before the transfer window closes.
"There will not be many signings," he said during Tottenham's pre-season tour in the United States on Friday.
"We have a very good and big squad. Last summer the club made a big effort during the window and I believe in these players. We are always looking to improve but we don't expect big change."