The south-coast club, who finished eighth in the Premier League last term, have experienced an alarming player exodus during the off-season, with a number of high-profile stars moving on.
Rickie Lambert, Adam Lallana and Dejan Lovren have all signed for Liverpool, while young defensive duo Luke Shaw and Calum Chambers have joined Manchester United and Arsenal respectively.
With manager Mauricio Pochettino also departing for Tottenham, to be replaced by Ronald Koeman, many are tipping Southampton to struggle after being shorn of so many key players.
It had been rumoured that Rodriguez and Schneiderlin were also set for the exit door, with Pochettino said to be keen to take them to White Hart Lane, but Krueger moved to dismiss such talk on Tuesday.
"They are part of the core of our team," he told Sky Sports News. "They are not for sale and will be part of the club as we enter the new season.
"They are excited along with the rest of the squad to continue moving forward."
Krueger said he appreciated the concern voiced by fans about the number of players leaving, but he assured supporters the club were in the process of finding replacements.
"I understand the fans' frustration," he added. "We are excited to continue our rebuilding process, in the next few weeks we will have players coming in.
"September is judgement day. We are in a process at the moment and that is far from over.
"We have to continue to try and get the right players. Ronald Koeman has done an outstanding job. We know that we need more players and more depth to our line-up but it is not about today or tomorrow, but getting the right player on the right deal.
"We want to give Ronald Koeman the players necessary. We will make deals at the right time for the club.
"We are very close to a few deals but I don't want to put timsecales on it. For Ronald and his staff it is much better to get them in tomorrow so he can integrate them into his squad, but we are working as quickly as possible to make them a fact.
"We are not just building a squad but building people and we are looking at values with the players we bring to really have a squad where everyone is pulling together in same direction."
