The highly-rated defender, 18, has been repeatedly linked with a move away from the Saints in recent months.
However, Ward-Prowse believes that Shaw should remain at St Mary's Stadium in order to develop his career.
"Obviously there is a little bit of banter flying around about the headlines, but that is just normal in football," the midfielder is quoted as saying by Sky Sports News.
"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."
Shaw has made 22 appearances for Southampton so far this season.