Goretzka has scored six goals in 14 appearances for club and country so far this season.
Rumours regarding Jose Mourinho and Manchester United's apparent interest began circulating across the English press on Saturday (2 December), with the 22-year-old free to begin negotiating a pre-contract agreement with overseas suitors from 1 January.
However, Goretzka's future at the Veltins Arena is in serious doubt as he's in the final year of his contract and he's failed to agree terms over an extension despite Schalke's best efforts to tie him down to a new deal.
The Germany worldwide has been linked with a move to the Emirates for some time and with his contract set to expire at the end of the season, many consider him to be Arsenal bound. I am a person who is very meticulous in such decisions. "The final decision will be made in January". So I need time.
"We feel that England, because of the amount of money you have with TV rights, young talented players like Leroy Sane and [Schalke's] Leon Goretzka are moving to England and this is not good for our league but also for the quality of our game", said Bierhoff.
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.