The 24-year-old France international posted a tweet on Tuesday that suggested he was unhappy to be told his future lay at St Mary's, and he has followed that up with an official transfer request despite reports he has no release clause and three years left to run on his contract.
Saints lost manager Mauricio Pochettino to Tottenham at the start of the summer and several big-money sales have followed - Luke Shaw joining Manchester United for £27million, Adam Lallana and Rickie Lambert joining Liverpool for £25m and £4m respectively, and Calum Chambers joining Arsenal for £16m.
Pochettino is reportedly keen for Schneiderlin and Southampton striker Jay Rodriguez to join him at White Hart Lane but executive director Les Reed and chairman Ralph Krueger are adamant that there will be no further departures from the club, prompting Schneiderlin to demand a move.
Spurs are thought to be ready to pay £20m for Schneiderlin, who said via his Twitter account in the wake of talks over his future: "6 years of an amazing journey #saintsfc DESTROYED in 1 hour !!!(sic)."
Schneiderlin came through the youth ranks at Strasbourg before Southampton paid £1.2m for his services in 2008.