The 34-year-old has been without a club since leaving Real Madrid at the end of last season and could have offered experience in both central defence and at left-back.
However, the Manchester Evening News reports that United believe Alaba has regressed in recent years and have opted not to pursue him.
United had identified left-back as an area requiring reinforcement during the summer, with the intention of providing competition for Luke Shaw.
No new player was ultimately signed in that position, leaving Shaw under increased pressure to remain fit, particularly with the club returning to the Champions League.
Alaba's recent fitness record appears to have contributed to his reduced market appeal. He suffered a serious ACL injury in December 2023 and has subsequently missed 109 matches for club and country across the last three seasons.
His injury struggles limited him to a supporting role at Real Madrid in 2025/26, when he featured 16 times in all competitions and started only six matches.
Despite those difficulties, Alaba remains a decorated defender. He earned UEFA Team of the Year recognition three times during his Bayern Munich career and was included in LaLiga's Team of the Season for 2021/22 after helping Real Madrid win the Spanish title.
He also captained Austria at the World Cup, starting all four matches before their elimination by eventual champions Spain in the Round of 32.
Manchester United surrendered their advantage to draw 1-1 with Tottenham Hotspur at Old Trafford on Saturday evening, missing the opportunity to claim their second Premier League win of the campaign.
Chelsea bounced back from their defeat before the international break with a convincing 5-1 Premier League victory over Bournemouth at Stamford Bridge, as Jordan Henderson scored his first goals for the club.
Arsenal came from behind to secure a hard-fought 2-1 victory over Leeds United at the Emirates Stadium on Saturday, showing resilience to claim maximum points after falling behind in the second half.
Cole Palmer has signed a one-year contract extension with Chelsea, keeping the England international at Stamford Bridge until 2034.
