Blackburn have signed defender Doneil Henry on a month's loan from West Ham.
Miles Addison has joined Blackpool on a month's loan from Bournemouth.
The highly-rated 18-year-old has caught the eye of a number of top clubs in Europe this season, with Chelsea reported to be among the interested suitors.
Shaw has already made 43 first-team appearances for the Saints and is expected to be handed his first England call-up sooner rather than later.
Pochettino has welcomed the interest in Shaw, but he has insisted the club will reject all offers for the youngster when the transfer window opens next week.
"It is a very clear situation," the Saints boss said. "The player wants to stay, the club is not willing to sell.
"What we also need to consider is that he is an 18-year-old player, that he is still maturing, still progressing. He is still learning how to be an experienced player.
"We need to be very calm about the situation. It has taken his some time to mature as a player and I think all these rumours and all this speculation around him is not beneficial for him. I think it is negative for him.
"I think it is very clear what the project here at Southampton is. Our project is about young players and Luke Shaw is a prime example of someone who has come through the ranks at this club.
"Again, the player is just not for sale. Again, he wants to stay, so there is no Luke Shaw case."
Shaw celebrated his 18th birthday by signing a new five-year deal in July, and he recently responded to speculation over his future by claiming he was "not even thinking about moving".
The likes of Adam Lallana, Rickie Lambert and Jay Rodriguez have also been linked with moves after impressing for England this year, but Pochettino added: "I think many of our players have recently been in the spotlight.
"I think all of these players, all of my players, are going through new experiences that they have to adapt to, have to get used to.
"They have to live with these new experiences, new situations. We need to be able to manage the situation. This is also part of football, not just playing.
"We need to assimilate, need to adapt. We are going through a bad run of results of late (six matches without a win), but again with calm and work we need to get back into how we know we can play and perform."