The Austria defender is demanding a mammoth £400,000-a-week to stay at the German Champions League winners, says The Sun.
Both Premier League rivals would love to add the player to their ranks.
Alaba, 28, can play at centre-half or left-back and is rated one of the world's top defenders.
United need a partner for Harry Maguire at the back - but would have to shatter their £350,000-a-week pay ceiling to land him.
They also need competition for Benjamin Mendy at left-back, who has struggled with injuries.