The Belgium international has failed to make the desired impact at Old Trafford since his memorable breakthrough in 2013-14, spending the whole of last season on loan at relegated Sunderland.
Januzaj has been heavily tipped to make an exit in recent weeks, with Sociedad reportedly joined by Roma and Celtic in showing an interest, but the Red Devils are said to be holding out for a fee of close to £10m.
Sociedad chief Aperribay has confirmed that his side are keen to bring the 22-year-old on board, though it is down to Man United to determine whether or not they are willing to sell.
"It's true that we are interested but we are not in talks with Manchester or with him," he told Mundo Deportivo. "We are waiting for the decision of Manchester United and then we will act. There are more teams interested in him and his signing won't be easy."
Januzaj, who has also previously spent time on loan with Borussia Dortmund, failed to score in 25 Premier League outings for Sunderland last season.