Schneiderlin and team-mate Jay Rodriguez are being pursued by new Spurs boss Mauricio Pochettino, who left St Mary’s Stadium for north London earlier this summer, and a deal was understood to be close.
But Krueger told Sky Sports News on Tuesday that "specifically to Rodriguez and Schneiderlin, they will not be going anywhere" as the Saints look to end a slew of high-profile sales.
The midfielder wrote on Twitter: "[Six] years of an amazing journey #saintsfc DESTROYED in 1 hour !!!"
6 years of an amazing journey #saintsfc DESTROYED in 1 hour !!!— Morgan Schneiderlin (@SchneiderlinMo4) July 29, 2014
Arsenal were also keen to make good on a long-standing interest in the France international this summer but a desire to reunite with Pochettino, who led the Saints to eighth place in the Premier League last season, looked to have swayed Schneiderlin towards White Hart Lane.
First-team stars Rickie Lambert, Adam Lallana, Luke Shaw, Dejan Lovren and Calum Chambers have all already left Southampton this summer.
New manager Ronald Koeman has brought in Dusan Tadic and Graziano Pelle from the Eredivisie as he starts rebuilding the squad but the increasing frustration from fans as last season's stars are sold appears to have provoked the club's leadership into putting their foot down.
Schneiderlin has been a regular in the Saints setup since joining from Strasbourg in 2008 and was a pivotal part of their rise from League One to the top half of the Premier League, earning a place in France's World Cup squad earlier this summer.