Shaw joined the Reds on 27 June to become the most expensive teenager in world football, signing a four-year contract that will keep him at the club until June 2018.
Neville is the 19-year-olds's coach with England and, having watched him at close quarters during this summer's World Cup in Brazil, the Treble-winner is struggling to contain his enthusiasm for what the future might hold for the Reds' teenage prodigy.
"I am trying to keep guarded here about the size of talent that exists in this footballer," Gary told the Manchester Evening News. "You are talking about brilliant potential.
"The reason United spent £27m on a left-back at his age is because they see the huge talent and I can only endorse that talent. You have to watch him at close hand to realise that this is an incredible and hugely talented football player. Luke Shaw is fantastic."
Shaw has built a reputation as one of the Premier League's most exciting young stars as a result of his excellent performances with Southampton, where he was handed a first-team debut aged 16 before taking his top-flight bow a year later in the 2012/13 season.