United manager Jose Mourinho was reported to be interested in the 22-year-old Sweden centre-back.
However, BBC Sport understands the form of Phil Jones and Marcos Rojo in central defence has persuaded manager Jose Mourinho he does not need to buy.
The Portuguese also has cover at centre-back in Eric Bailly, Chris Smalling and Daley Blind.
Reports from Portugal had claimed Lindelof would become the club's most expensive all-time defender, costing between £38m and £42m, and that he had been assigned a squad number at Old Trafford,
Since Jones and Rojo were paired together for the first time in the 3-1 win against Swansea on 6 November, United are unbeaten for 11 games, one short of equalling their best run since Sir Alex Ferguson retired in 2013.
Jones and Rojo have been in central defence together for nine of those matches, when they have conceded seven goals.
Manchester United will not make a move for Benfica defender Victor Lindelof during the January transfer window.