Goretzka has developed in to one of the most highly-rated all-round midfielders in Europe since joining Schalke from boyhood club Bochum in the summer of 2013.
Schalke remain eager to keep hold of Goretzka.
Along with Bayern, all of Manchester City, Tottenham, Arsenal, Liverpool, Juventus and Barcelona have been linked with moves for Goretzka, with the Gunners having reportedly already set up negotiations with the German's representatives for January.
Responding to rumours about his future, the 22-year-old said: "I have to find out for myself what the next step should be". I am a person who is very meticulous in such decisions.
"[My next club] is not a matter of money, I only need to decide what's the best solution for me".
"There doesn't exist a deadline, but I think we are in the final phase", the player revealed when quizzed about the situation.
The likes of Joel Matip, Sead Kolasinac and Eric Choupo-Moting have pursued Bosman moves to the Premier League previously, and there is every chance that Goretzka could follow the same suite as Schalke are prepared to risk him for the final six months of his contract.
Goretzka hasn't confirmed that there is interest from United, or confirmed that he is interested in moving to Old Trafford.
United, now second in the Premier League, hope to use their improved status and Champions League football, to entice Goretzka to move to Old Trafford ahead of Premier League rivals Arsenal, Tottenham and Liverpool.