Shaw is currently in no man's land at Old Trafford, having played just two games in all competitions in the 2017/18 season so far, both of which came in the League Cup.
While he is a natural left-back, manager Jose Mourinho has preferred to play the likes of Ashley Young, Matteo Darmian and Daley Blind over him in the Premier League.
And with a total of just 47 minutes of first-team football this season, the 22-year-old's future under Mourinho looks bleak, especially with his physical and mental capabilities being called into question.
The Spanish manager believes Shaw could reignite his career with a move to Tyneside where he will be guaranteed first-team action.
Benitez understands that a permanent move is unlikely with the left-back said to be earning around £130,000 per-week, but believes a loan move in the January transfer window is feasible.
However, he will face competition for Shaw as his former team Southampton are also said to be interested as they seek to replace Ryan Bertrand, if he potentially moves to Manchester City.
Turkish giants Fenerbahce were also reported to be keen on signing Shaw on loan but the player had no interest in the move.
United recently took up the one-year option on Shaw's contract, tying him down to the club until June 2019, which meant the England international could not leave on a free transfer next summer.