Wan-Bissaka has been granted extra leave after returning from a holiday in Dubai.
ESPN has contacted United about whether the former Crystal Palace player had permission to travel to Dubai.
United begin the 2020-21 campaign against Palace on Sept. 19, a game for which Wan-Bissaka is now a doubt.
The club were given permission to start the season late by the Premier League after reaching the Europa League semifinals meant that they were in action until Aug. 16.
United were originally set to face Burnley away on the opening weekend.
Wan-Bissaka started 34 of United's 38 Premier League games last season as the club finished third in the Premier League.