Shaw, 18, has attracted rave reviews for his performances at left-back this season, impressing yet again in Tuesday's 2-2 draw with Arsenal, and he has been linked with both Manchester United and Chelsea.
But Ward-Prowse, only 19 himself, is confident Shaw will still be at St Mary's when the transfer window closes on Friday.
"Obviously there is a little bit of banter flying around about the headlines, but that is just normal in football," he said.
"His feet are on the ground, his head is in at the right place at the moment, and he put in a great performance against Arsenal.
"He is settled, that is the main thing. You can see the fans love him as well, which is a good thing. This is the best place to be, at the moment."
Morale still high at Southampton
However, club-record signing Dani Osvaldo may be set to leave, having been suspended for two weeks after instigating a training ground scuffle with Jose Fonte.
Ward-Prowse said: "It hasn't really affected us in a bad way.
"I think the camaraderie in the camp and everyone's positivity has resulted in us ignoring those off-the-field issues.
"Like you saw against Arsenal and against Yeovil (in the FA Cup) at the weekend, our performances have not been affected."
Ward-Prowse came off the bench during the entertaining 2-2 draw with the Gunners, in which Southampton led 1-0 before having to come back from 2-1 down.
"I think, in the end, it was a good point," he said. "
"All the lads are disappointed to lose out to two goals early in the second half, but we fought back and showed great spirit.
"It was frustrating, as we outplayed them in the first half. But we stuck in there, showed character, and got a point."