Reports in France have suggested the 22-year-old left-back could be in line to replace Patrice Evra at Old Trafford, while Italian newspaper Tuttosports claim the player is among the Rossoneri's January targets.
During the summer transfer window St Etienne were in talks with Premier League clubs Liverpool and Queens Park Rangers, as well as Serie A side Torino regarding the wing-back.
However, despite the high-profile links Ghoulam remains focussed on giving his all for St Etienne, who are currently seventh in French top-flight.
"I would love to finish the season her now, it has been a very difficult time for me in the summer with the Torino affair," he told Sky Sports.
"However, things go quickly in football so we never know what is next.
"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, who joined the St Etienne development system at seven-years-old, has played 90 minutes in the French club's last seven outings and registered his first senior goal with a penalty against Marseille in September.