These days, the left-back is a regular in Mauricio Pochettino's starting XI, and his list of admirers continues to grow.
But why are so many top-flight clubs clamouring for his signature? Apart from being young, talented, English and part of a defence that has only conceded 10 goals all season...
Below, we look back at Shaw's rise to fame and discuss all the gossip linking him with a move away from St Mary's.
Shaw's Beginnings—Chelsea Miss Out
The young left-back joined Southampton aged eight. As reported by the Mirror's Matt Law, he could have joined Chelsea, but the club felt he was too small and let him go after spending time at their youth academy.
Shaw's development and steady progress through the Southampton ranks, paired with appearances for England's U16 and U17 teams, were already attracting him admirers.
At 17, while still an unused first-team substitute, former Saints manager Nigel Adkins was forced to bat away interest from Arsenal, Chelsea and Manchester City. He told BBC Solent, via BBC Sport: "Luke Shaw is a big part of our future plans. We have got no intention believe you me of letting any of our young players move on."
These players all left the side before turning 18, moving on to so-called bigger clubs and leaving the Saints behind.
In the past, Southampton have been a selling side, something that Pochettino is keen to shift away from. The manager told ESPN FC last season: "I think there is a clear path that we want to be on. It is clear the club that I am at wants to keep growing and move forward and it has shown just that by getting new contracts to some very important players in the club."
Shaw's breakout season was in 2012/13, when he was drafted into the first team. He made his Premier League debut against West Bromwich Albion and went on to make 24 more appearances that term.
That season, teammate Adam Lallana told the Daily Mail's Sam Cunningham:
The calmness he possesses for a 17-year-old is astonishing. He has got a great left foot on him and he has bedded in really well. He has got to keep up his fitness and he is going to go far in the game.
There a big similarities between him and Bale. That is what people have been saying but he knows he has got to keep his feet on the ground and has a lot to learn but he is going to improve a lot with us, I can tell.
Also described as "technically very gifted" by FA director of football development Sir Trevor Brooking, seen here in an article by The Guardian's Louise Taylor and Dominic Fifield—Shaw seemingly has it all.
He is a natural defender. At 6'1" and with a stocky frame, Shaw is very strong. He's already a great tackler, holds the ball up well and has an incredible turn of pace, as seen in this surging run that he made against Chelsea last season:
Part of Shaw's allure is the confidence that he displays in every fixture. He reads the game really well and seems unfazed by pretty much anything. He is calm on the ball, assured and not afraid to take risks with his marauding runs down the wing. This, inevitably, is what has drawn comparisons between him and Bale.
The Daily Mail's Elliott Bretland reported from Stamford Bridge last weekend when Southampton travelled to take on Chelsea. In his piece, titled "Luke Shaw watch," he wrote: "Shaw has a football brain way beyond his years. For someone so young he reads the game brilliantly and seems to make sensible judgements. He doesn't launch into tackles but patiently waits to make a challenge - often dispossessing his opponent."
January 2014—The Gossip
Five-year contract or not, there is a steady flow of speculation linking Shaw with a move away from the South Coast. According to Neil Fissler in the Express, Southampton may have to brace themselves for a £30 million bid from Chelsea in the new year.
The Blues, who need a long-term replacement for 32-year-old Ashley Cole, failed with two bids for Shaw in the last two transfer windows, according to Fissler.
In the Mirror, Dave Kidd reports that Tottenham Hotspur are preparing an offer to bring the left-back to White Hart Lane in January. Andre-Villas Boas' side are in desperate need of someone in this position after losing Danny Rose to injury.
The Reality—Shaw's Five-Year Contract
You never know what may happen, but it looks like Shaw may continue to eschew interest from clubs in the higher echelons of the Premier League.
Over the summer, when he signed a new five-year contract on his 18th birthday, the England U21 international told Southampton's official website: "I've been here since I was eight and I've loved every single moment of it. I want to stay at this Club, and signing this contract means I'm here for another five years."