The 19 year-old has been outstanding for Leipzig this season, with his form attracting enquiries from Europe's biggest clubs.
United are making their move as face losing the battle for Bournemouth attacker Antoine Semenyo to Manchester City.
TalkSPORT says United are weighing up a January bid for Diomande.
Diomande was born in Ivory Coast and moved to Florida in 2022, where he played on a university team for three years. He left for Leganés in 2025, but after six months he switched to Leipzig, where he has performed excellently this season.
For Leipzig, they're insisting the winger won't leave for less than €100m.
RBL chief Marcel Schafer recently stated: "Yan has adapted very quickly to us in the Bundesliga, especially considering that he is only in his first year as a professional and is very young.
"He is on the right track, but like all our other players, he still has a lot of potential to develop further. We are very much looking forward to realizing that potential together in the coming years."