The Swiss youngster was previously linked with a move to Old Trafford.
The 19-year-old joins the Bundesliga side for a reported £20 million – as quoted by the Guardian – after they fought off stiff competition from some of Europe’s biggest clubs.
His switch to Germany now means United will have to look elsewhere if they intend to bolster their attack ahead of the new campaign.
Jose Mourinho typically spends big upon arriving at a new club and this summer should be no different at Old Trafford.
Mkhitaryan is a player who would instantly impact the first-team and add real star quality to an inexperienced Red Devils attack.
Embolo, on the other hand, is raw potential at this point and is perhaps best served learning the game in a less scrutinised environment.
Reaction from United fans to their apparent failure to secure a key target was widespread on Twitter and we have provided a selection below:
Why we didn't go for embolo is beyond me. ED WOODY AGAIN SORT THAT HEAD OUT!!!!— Vishal Patel (@KINGV1997) June 26, 2016
Embolo moving to Schalke 04 for 25 million... One that got away— Will (@TouchOfBerbatov) June 26, 2016
We're signing Zlatan and Mkhitaryan but rival fans still think Embolo rejected us.— Jonah (@MuellerHolic) June 26, 2016
One speculation thrown into the bin...Thanks Embolo for being decisive. Not actually what's needed at #mufc— M A R K (@Marky210) June 26, 2016