The 22-year-old bagged his fourth goal of the season in the 2-0 win under the watchful eye of Barcelona technical secretary Robert Fernandez, who has been a regular at Schalke fixtures.
The midfielder is due to fall out of contract at the end of the season, but there is no sign of him penning a new one, leading to some of Europe's top clubs starting to form an orderly queue.
Barca are said to be heading it, but there is also interest from Liverpool and Juventus, who could make offers when the January transfer window re-opens.
Barca could turn to Goretzka if they miss out on Liverpool's Philippe Coutinho, while the Reds will want him should the Brazilian head to the Nou Camp.
The German international is likely to wait until the end of the season before making a decision unless Schalke attempt to recoup some cash by pushing for a transfer in January.