Pochettino was in charge at Southampton when the Frenchman first arrived in the Premier League and is allegedly now interested in signing him at White Hart Lane.
Spurs have had little encouragement from Man United so far and are also pursuing alternative targets such as Moussa Sissoko at Newcastle.
Schneiderlin has only played five minutes of league football under Mourinho this season and is currently behind the likes of Paul Pogba, Marouane Fellaini and Michael Carrick in United’s midfield pecking order.
Mourinho insisted last week he was happy with his squad and wasn’t looking to sell or buy any new players.
The Portuguese boss has also refused to strengthen Premier League rivals this summer and has turned down any interest from English clubs in Phil Jones.
Schneiderlin will be hoping for a first-team role rather than just being used in competitions such as the domestic cups and the Europa League, but Pochettino will be keeping a close eye on his position at United and could be looking to return in the January transfer window if the Frenchman isn’t able to find a place on Mourinho’s side.