The Spanish outfit have tabled a bid of £10m for the Belgium winger in the hope of securing a deal.
United bosses are mulling over the offer but are expected to allow Januzaj to restart his faltering career in Spain.
Januzaj burst onto the scene when David Moyes was United boss.
The winger was hailed as one of the brightest prospects in Europe and was tipped for greatness.
But when Moyes was sacked and Louis van Gaal replaced hMs as United boss his career started to stall.
Van Gaal didn’t rate him and allowed him to join Borussia Dortmund on loan.
But he failed to start a single Bundesliga game and returned to United to face a gloomy future.
Jose Mourinho told him he wasn’t part of his long-term plans and allowed him to join Sunderland on a season-long loan last summer.
The 22-year-old vowed to prove his doubters wrong but he also had a miserable time at the Stadium of Light.
He struggled with several injuries and made just 18 league starts in a campaign that saw the Black Cats relegated to the Championship.
He has been left kicking his heels since the end of the season but Sociedad have now come in for him with the chance of a fresh start elsewhere.
The Belgium international, who has won six caps, signed for United from Anderlecht as a youth player in 2011.
