The 25-year-old joined Frankfurt on a permanent deal last summer and has been in impressive form during the 2020-21 campaign, scoring 19 times in 22 appearances in all competitions.
The Portugal international found it difficult to make his mark at AC Milan between 2017 and 2020 but has now managed 35 goals in 59 outings for his current team, including a loan spell during the 2019-20 campaign.
United are thought to be keen to bring a new centre-forward to the club, with Borussia Dortmund's Erling Braut Haaland an option, but the likes of Real Madrid and Barcelona are also said to be in the mix for his services.
According to Sky Deutschland, Ole Gunnar Solskjaer's side have identified Silva as a possible acquisition, with the second-highest scorer in this season's Bundesliga potentially available for a reasonable price.
The forward also has an impressive record at international level - where he plays alongside United attacker Bruno Fernandes - finding the back of the net on 16 occasions in 37 appearances.
Silva's current deal with Die Adler is due to run until the summer of 2023.