It has been speculated that the duo would be the next players to leave St Mary’s following the double departure of Dejan Lovren and Calum Chambers in recent days, but the Canadian was quick to dismiss that prospect.
Speaking to Sky Sports News, Krueger insisted that Rodriguez and Schneiderlin are going nowhere, adding that the five players who have departed this summer were allowed to do so “in the best interests of the club”.
“Jay Rodriguez and and Morgan Schneiderlin are not for sale, and they will be a part of our club as we enter the new season,” said the chairman.
“They are part of the core that we have decided to keep at Southampton. In and around Jay, Morgan and the rest of our core players, we’re excited to continue to build forward.
“Quite clearly, we entered the transfer window with a plan,” he continued.
“We have a clear strategic approach to this summer, and we did not put any players for sale. What we did say was that we would watch the process, we would listen and we would look for how the team would evolve out of our rebuild.
“It was quite clear that we had multiple players interested in taking a shortcut to Champions League football. We saw that building a little bit before the World Cup and clearly we stayed patient and didn’t make quick deals in any shape or form
“We set premiums on the players, and we’ve reached those premiums. Our executive level has been working outstanding hours and has put good deals together that give us a strong position to reinvest and a strong position to rebuild.
“It was in the best interests of the club and the best interests of our rebuild to make these deals and to continue to build forward with players and a team that wants to go the hard way into Europe.
“None of these deals were made on financial reasons alone. We were completely ready to have players stay at Southampton against their desire if we didn’t reach our target prices. These were not financial decisions.
“I can understand some frustration in and around our fans, but we needed to stay silent in order to bring in the best deals for the club.”
Krueger says the focus is now on using the funds generated by those sales to strengthen the squad available to new manager Ronald Koeman.
“Now we have finances and we are excited to continue in the rebuilding process,” he enthused.
“Over the next few weeks we will have players coming in and we will make transfers to strengthen the squad. Our plan is to get the right deals and the right players.
“Ronald Koeman has done an outstanding job with his staff thus far in pre-season, and we’re extremely pleased with the work that’s going on at St Mary’s.
“We know that we’re going the right way, but we also know that he needs more players and that we need more depth in our line-up.
“It’s not about getting them in today or tomorrow, but about getting in the right players and the right deals that fit the way Ronald wants to play and the way we want to play.
“We want to continue to play attractive football at Southampton, and we want to give them the players that are necessary.
“We would all like to see them sooner rather than later, but we will make deals at the time when we feel they are right for the club.
“I believe that we are very close to a few deals and that, by the time we kick off against Liverpool, for Ronald and his staff, it is much better if we get them in tomorrow so that he can begin the process of building them and integrating them into the team and the system of play.
“We are working as quickly as possible to make that a fact, but I don’t like to speak in definites when I don’t know them. People need to realise that we are in a process and the match is far from over.”