Per Grant Wahl of Sports Illustrated the Bavarians have "significant interest" in the American. Kicker (h/t CBS Sports' Roger Gonzalez) previously reported on the links between Pulisic and Bayern earlier this year.
Dortmund director Michael Zorc recently told Kicker a January exit is ruled out, but the 20-year-old has said he will talk to the club during the winter break regarding his future, per Sky Sports: "I'm still focused on Dortmund. We are doing great this season. Once the break comes [in January], that is always when I will have to discuss with Dortmund and see about my future."
Pulisic has emerged as the top American talent and one of the Bundesliga's most exciting youngsters, leading to plenty of transfer speculation over the years. As with most budding stars in Germany there have been ample links with Bayern, as well as rumours he could be headed to England soon.
Liverpool were seen as favourites to land his signature due to the presence of former Dortmund boss Jurgen Klopp, but Chelsea have emerged as the front-runners of late. Per the Mirror's John Richardson (h/t Anfield HQ) the two clubs are set for a serious battle:
Dortmund have done a fine job developing the forward, but his growth appears to have stagnated somewhat of late. Per WhoScored.com, he has only played 379 Bundesliga minutes so far this season, falling behind Jadon Sancho in the pecking order. He has scored just a single goal in the German top division this campaign.
A change of scenery at some point in the near future seems likely, and Bayern would present an intriguing destination. The club has a history of raiding Dortmund for their best players, with Robert Lewandowski, Mario Gotze and Mats Hummels all making the switch in recent years, and they have a clear need for youth out wide.
Franck Ribery and Arjen Robben have locked down the wings for years but are now 35 and 34 years old, respectively, and there are plenty of questions behind those two. Kingsley Coman's career has been sidetracked by several major injuries, and Alphonso Davies is just 18 and seemingly not ready to make the leap.
As noted by Wahl, Bayern have invested strongly in building their brand in the United States, and adding Pulisic would be a big next step. He's already the national team's most marketable star and youngest captain in the modern era:
Chelsea may face a two-year transfer ban that could knock them out of the running for Pulisic come the summer, per Wahl. They may choose to push for a January deal as a result, even if Dortmund are unwilling to sell and likely to hold out for a huge fee.
Bayern could also get involved in January as they'll be desperate to add to their squad following a poor start to the season.