It has been reported in the past that La Liga giants Barcelona and Real Madrid were in the race for the services of the highly-rated 29-year-old.
Kimmich has made seven appearances in the Bundesliga for Bayern Munich so far this season, assisting one goal, with the Bavarian side making a good start to the domestic term.
Under the reign of former Burnley head coach Vincent Kompany, the German giants have moved to the summit of the Bundesliga standings, ahead of second-placed RB Leipzig.
Since making the permanent switch from fellow German side Stuttgart in the summer of 2015, Kimmich has featured on 400 occasions for Bayern Munich, scoring 42 times.
PSG, Man City suffer Kimmich blow?
According to transfer specialist Fabrizio Romano, Bayern Munich are making serious steps towards securing the long-term future of enforcer Kimmich.
The report claims that the Bavarian club are now more confident of agreeing a new contract with the 29-year-old, who has been linked with a move away in recent times.
It is understood that negotiations between the player and the Allianz Arena outfit are underway, with Kimmich more receptive to extending his stay at the club compared to last season.
Such developments come as a major blow to the ambitions of Paris Saint-Germain and Manchester City, two sides who were linked with the 95-time international earlier in the calendar year.
Bayern Munich want Kimmich to be a key part and the face of the new project at the club under the forward-thinking stewardship of former Man City defender Kompany.
Man City scrambling for replacements
Tussling prior to a corner kick with Arsenal's Thomas Partey in a Premier League match on September 22, Man City's Rodri suffered a season-ending knee injury.
As a result, Pep Guardiola's side are understandably set to enter the market for a new midfield lynchpin during the upcoming January transfer window.
Winning numerous Bundesliga titles and a Champions League with Bayern Munich, Kimmich would represent an elite capture for the Premier League holders.