Tottenham had been in talks to bring the duo to White Hart Lane in a double deal, with new Spurs boss Mauricio Pochettino keen to be reunited with two players who flourished under his tutelage last season.
But the Saints chief has now categorically ruled out selling Schneiderlin and Rodriguez and is keen to end the ongoing exodus at the club, while Ronald Koeman says the pair are central to his plans for the future.
"Specifically to Rodriguez and Schneiderlin, they will not be going anywhere," Krueger told Sky Sports News.
"We see them as part of a core and the core we’ve got right now and in place is a core that is where Ronald [Koeman] would like to go and they a part of that core.
"Any reports that Rodriguez or Schneiderlin are leaving or we are in engaged in transfer conversations are totally off the mark. They will not be sold."
The club have already lost five players this summer, with Luke Shaw joining Manchester United, Rickie Lambert, Adam Lallana and Dejan Lovren all moving to Liverpool, and Arsenal signing Calum Chambers.
Southampton will receive over £100 million in transfer fees for those five players, but had been especially keen to ward off interest in Schneiderlin, offering the France international the captaincy and a pay rise.