According to Steve Millar in the Daily Star, Sky Blues manager Pep Guardiola sees Weigl as a potential long-term successor for Fernandinho, but the Bundesliga club are not prepared to let him go easily.
At 23, Weigl is 10 years younger than Fernandinho, who is now in the latter stages of his impressive career.
City have fantastic depth in most positions on the pitch, but they are lacking in the deep-lying midfield role, especially with Yaya Toure departing the club earlier this summer.
Per James Ducker in the Telegraph, Fred and Jorginho were both pursued by City previously in an attempt to bolster the engine room, but they ended up joining Manchester United and Manchester City, respectively.
Weigl has been a key player in Dortmund's first team since moving to the club in 2015, and he is also of interest to Paris Saint-Germain, per France Football (via Goal's Ronan Murphy):
He has already made 85 Bundesliga appearances for BVB and boasts numerous attributes that could see him flourish in the Premier League with City, including a fine passing range.
It is unlikely Germany international Weigl would immediately unseat Fernandinho in the first team were he to move to City in January.
But he would be able to learn from the Brazilian and settle into Guardiola's squad before eventually taking up a regular starting spot.