The former Liverpool and Chelsea boss is convinced the left-back is in desperate need of some regular game time and he will look to land him in January.
Shaw’s career has stalled under Jose Mourinho, with a lack of fitness and form limiting his involvement under the Portuguese.
Mourinho is believed to be open to him leaving on loan to another Premier League side and Benitez is keen on a short-term move for the 22-year-old, according to the Mirror.
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However, Benitez faces real competition to land the left-back, with Southampton and Tottenham Hotspur believed to be sniffing around, according to the Mirror.
Spurs boss Mauricio Pochettino worked with Shaw at St Mary’s and with Danny Rose out of favour at White Hart Lane, a swap deal could be on the cards.