The German TV channel claims the Red Devils have ‘specifically inquired about the player’s situation’.
United were reported last month in England to be monitoring Plea, with Leicester City also interested.
It appears United have stepped up their interest by making contact for the impressive striker.
Plea joined Gladbach from Nice in July 2018 for a club-record €23m and has proven to be an excellent signing.
This season, the 27-year-old has scored eight goals and contributed seven assists in 20 starts for Die Fohlen.
Plea has been largely overlooked by France boss Didier Deschamps despite his great form in the Bundesliga. He has just one cap for Les Bleus, having appearing for 10 minutes against Uruguay in November 2018.