Gabriel is a target for several clubs across Europe this summer, including Everton and Napoli.
More recent reports though suggested United were leading the bidding and had held talks over a €30m (£27m) swoop.
However, it seems United may have had a change of heart. The imminent club-record swoop of Jadon Sancho means United may need to spend the remainder of their budget more carefully.
With that in mind, United have welcomed Chris Smalling back in their fold. The 30-year-old is back at Carrington following a season's loan with Roma.
Smalling had hoped an extension could have been agreed to allow him to play in the conclusion of the Europa League. However, no agreement was reached, leaving the "gutted" player to express his dismay.