Sky Deutschland claims that United chief Ed Woodward has made contact with the player's representatives to test the water on a potential move to Old Trafford.
The 27-year-old has directly contributed to 15 goals in 22 Bundesliga appearances this season, scoring eight times himself and creating seven more and his form has alerted several clubs across Europe.
Arsenal and Tottenham Hotspur are also thought to be interested in the forward.
Plea is contracted to Monchengladbach until 2023, with the German outfit valuing the ace at around £21 million.
German outlet Express.de, via the Daily Star, reported last month that United had turned their interest to Plea. The report stated that the former Nice forward was "among a group of strikers to be examined" for the 2020-21 campaign with one of those believed to be Moussa Dembele.