United lost all three of their league games last month - 4-2 against Reading, 1-0 against Southampton and 2-1 at Norwich - but beat Doncaster 3-1 in the Checkatrade Trophy.
And Roberts' performances have seen him shortlisted for the award. The shortlist was decided by the Premier League's Football Development Panel after PL2 managers nominated the best performance by an opposing player in each of their league matches in September.
Roberts, 21, featured for Rafa Benítez's first team during pre-season and scored in United's opening two PL2 games of the campaign. He was also on target in Thursday's Premier League Cup win over Notts County.
Also nominated are Daniel Butterworth of Blackburn Rovers, Brighton & Hove Albion's Aaron Connolly, Louie Sibley of Derby County, Manchester City's Rabbi Matondo, Reading's Ryan East, Benjamin Mbunga-Kimpioka of Sunderland, Swansea City's Joe Lewis and Oliver Skipp of Tottenham Hotspur.
The panel will decide the winner, which will be announced on Friday 12 October.