Goretzka is out of contract next summer, and Schalke may be ready to sell in January, which could prompt City into making a move, according to Simon Mullock at the Sunday Mirror.
City are keen to inject some youth into their midfield, with Yaya Toure's time at the club coming towards an end and Fernandinho turning 33 next year.
The Bundesliga's Twitter account shows how effective Goretzka has been for Schalke this season:
However, Bundesliga correspondent Shane Burns says a move to Bayern is more likely and explains why City do not really need Goretzka:
Goretzka seems destined to leave Schalke, although it's unclear if the club will look to cash in during the January transfer window or keep hold of him for the rest of the season.
Meanwhile, Guardiola wants Van Aanholt in January to fill in for injured left-back Benjamin Mendy, per Mike McGrath at The Sun.
Guardiola has been using midfielder Fabian Delph in defence but "wants a specialist" and sees £12 million-rated Van Aanholt as easier to land than Southampton's Ryan Bertrand.
Manchester City's Twitter account showed how impressive Delph was in Saturday's win over Leicester City:
Van Aanholt has made eight appearances for Crystal Palace this season, but the club are bottom of the table, having conceded 24 goals in 12 appearances.
The 27-year-old picked up a hamstring injury in the draw with West Ham United on October 28 but had also put in a less-than-impressive performance, per football writer Jim Daly:
A City move for Van Aanholt would be a surprise, given that the Dutchman has not particularly shone this season. Delph has also been something of a revelation filling in for Mendy, and Guardiola has Danilo—who can play at left-back—as a further option.