The Scot was unveiled as manager of the San Sebastian club on Thursday, six months after being sacked by Manchester United, and is determined to rebuild the reputation he worked so hard to develop in 11 years at Everton.
Moyes is believed to be an admirer of the ex-Aston Villa and England player, who saw plenty of action during his unsuccessful reign in charge at the Manchester outfit. He has allegedly been told Young would join him in Spain if the two clubs can agree on a deal.
The 29-year-old has fallen down the pecking order under Louis van Gaal at Old Trafford and will be free to move on in January if he can find another team. The 29-year-old signed a five-year deal when he arrived at Old Trafford in 2011 but he is well aware that his chances of first-team action are going to be limited under new manager Louis van Gaal.
The winger has drastically underperformed since swapping Villa for United in the summer of 2011, yet following a remarkable pre-season, he looked guaranteed a role under Van Gaal. Nonetheless, he has made just four domestic appearances this term, and has done little to convince the Dutchman that he is worth a starting berth.
Sociedad have not given Moyes a definitive transfer budget as yet. However, he is a manager who is more than capable of working under financial restrictions. After all, he did so for over a decade at Goodison Park.
Young is an intelligent, versatile player, who possesses the skill set to thrive in La Liga. At the right price, he could be an excellent coup for Moyes as he kicks of his career in Spain.