The Blues expect competition from other elite European clubs to sign the United States international, including Paris Saint-Germain, but Liverpool have backed out of the race for the 20-year-old, despite having had an £11m ($14m) offer rejected in 2016.
Chelsea are keen to look to the future in their wide positions and are also aware that Eden Hazard's future remains in doubt, after he admitted an interest in moving to Real Madrid , with his contract at Stamford Bridge set to expire at the same time as Pulisic's at Dortmund.
Both Chelsea and Dortmund are trying to renew contracts for Hazard and Pulisic, with their current deals expiring in June 2020, but neither club are willing to allow their players to move in the January transfer window.
Chelsea's need to investigate the signing of a winger is added to by doubts over the future of wonderkid Callum Hudson-Odoi , while Willian and Pedro are both over 30.
Pulisic has faced an increased battle for game time at Dortmund with English starlet Jadon Sancho’s emergence adding to competition, as Marco Reus, Jacob Bruun Larsen and Marius Wolf all fight for starts at the Westfalenstadion.
The American, the youngest player to captain his country since the early 1990s, has already made over 100 appearances for Dortmund, scoring 15 goals and providing 24 assists.
Dortmund have been in fine form this season, even with Pulisic struggling with injuries, and have yet to lose, winning nine and drawing three of their opening 12 games of the campaign.
That leaves the club four points clear at the top of the table, while they are already nine ahead of crisis-hit Bayern Munich.
*Additional information provided by Sabrina Belalmi and Neil Jones.