Keown urged those at Emirates Stadium to make a move, with it obvious that the talented teenager was destined for big things.
Those calls fell on deaf ears and Shaw eventually joined United for £30 million ($39m) in the summer of 2014.
Keown told the Daily Mail when asked if that recall was deserved: "100 per cent. I actually would have taken him to the World Cup in Russia. There was enough time at the end of the season for Gareth Southgate to work with him, get him fit and help rebuild his confidence.
“We took him to the 2014 World Cup with a view to developing him into England’s first-choice left-back for 2018 but that did not materialise.
“I first watched him as a 16-year-old playing on a training pitch for Southampton against Reading. In the first 10 seconds, he whipped a ball across the box with such power and precision that I just thought, ‘Wow'.
“I was standing next to an Arsenal scout and I immediately said, ‘You’ve got to sign him'.
“Rarely had I seen a 16-year-old play with such certainty. In recent years he lost that from his game but it is coming back. This summer Jose Mourinho has given him his support and as a result Shaw has flourished.
“If Shaw keeps getting down that wing and keeps making things happen, then there is no reason why he could not be England’s equivalent of Benjamin Mendy for Manchester City.”
Shaw has made just 46 Premier League appearances for United, and 69 across all competitions, but does now appear to be Mourinho’s favoured option in what has been a problematic left-back berth.