The Red Devils have seemingly thrown their hat into the ring for the in-demand 22-year-old, and have now joined the likes of Barcelona, Liverpool and Arsenal in keeping tabs on his situation in Gelsenkirchen.
Goretzka's deal with Schalke expires next June, but despite the Bundesliga club's desire to retain his services, he has ruled out penning a new contract that would make him the highest paid player in the club's history.
Goretzka is free to talk to foreign teams from 1st January and would be able to shake hands on a pre-contract agreement with any side outside of Germany.
That has led to an almighty scramble for the midfielder's signature with a whole host of European giants now circling.
Barcelona, Liverpool and Arsenal have all been linked with the Germany international since the summer transfer window closed, and the trio now face even more competition for Goretzka if United's interest is as concrete as Sky make out.
It would be very Mourinho-esque to have stolen a march on his competitors, and sign the likes of Mesut Özil and Leon Goretzka before anyone really knew what was going on. Just sayin' ..— Jonas Giæver (@CheGiaevara) December 2, 2017
Jose Mourinho has a plethora of talented attackers at his disposal, but would be remiss to pass up the opportunity to secure one of Europe's brightest talents for nothing.
With rumours about Marouane Fellaini's and Henrikh Mkhitaryan's future at Old Trafford uncertain - the former out of contract and the latter drawing criticism from Mourinho for his form - Goretzka's potential arrival would boost competition for places in the Red Devils' senior squad.
Schalke have already seen other top talents such as Joel Matip and Sead Kolasinac trade life in Germany for the Premier League in recent times, with the duo leaving the club on a Bosman for Liverpool and Arsenal respectively.
Die Knappen would be furious to lose another youth product for no money, but there is nothing they can do to prevent Goretzka from chancing his hand overseas.
Goretzka has scored 19 goals and notched 13 assists in 129 appearances for Schalke since he joined the first team set up at Veltins-Arena in the summer of 2013.