The 22-year-old has been in sensational form for the Ligue 1 side of late, developing into one of the division’s top talents.
But, Saint-Etienne look set to lose the Algerian ace at the end of the season, with his current contract set to expire.
This has alerted United, who are desperate to find a long-term replacement for Patrice Evra.
The Frenchman has been one of the Red Devils’ more dependable performers in recent years, but is edging towards a return to his homeland at the end of the season when his deal at Old Trafford ends.
Ghoulam is seen as a good replacement, but the Premier League champions will have to battle off interest from Roma.
Reports suggest that the Serie A side are watching the defender, and that they may launch a cut-price January move for his services.
Despite interest from many big clubs, Ghoulam has previously admitted that he is flattered by rumours of United’s interest.
“Manchester United? You are always flattered when such a big club is linked with you but I do not want to dream, the reality is to give 100 per-cent for St Etienne and see what will happen next,” Ghoulam said.