The 18-year-old has risen to prominence since breaking into Nigel Adkins' starting XI last season, and his sustained form under Mauricio Pochettino earned him a first England cap against Denmark.
Everton's Leighton Baines and Chelsea's Ashley Cole are also vying for the left-back slot in Roy Hodgson's squad for Brazil but, despite being tipped to get the nod, Shaw admits he is trying to avoid getting mixed up in the media frenzy.
"I try to ignore that sort of stuff, the media attention, as obviously it is going to happen," the full-back told reporters.
"I spoke with Roy about it and he said that 'there is nothing you can do about it, this stuff is going to happen'.
"I am going to keep pushing myself and see what happens at the end of the season."
Shaw has made 28 appearances for Southampton during the current campaign, but is yet to register his first senior goal.