The Evening Standard is citing sources in Germany as claiming that the Blues held talks with Dortmund last Friday about the possibility of signing the highly-rated winger.
The same story claims that Chelsea FC made an offer to try and sign the USA international as they look to try and land him in the January transfer window.
According to the same report, Dortmund are likely to hold out for a fee of around £70m – even though the player only has 18 months left on his current deal with the Bundesliga side.
The article also says that the 20-year-old himself is refusing to discuss a new deal with Dortmund as things stand.
It is also claimed that Dortmund are maintaining that Pulisic will stay at the club until the end of the season.
Pulisic is widely regarded as one of the top young talents in Europe and he has scored one goal and made two assists in eight Bundesliga games so far this term.
His last appearance for the club claim during the goalless draw with Club Bruges in the Champions League on 28 November.
Meanwhile, Chelsea FC are currently preparing for their trip to Wolverhampton on Wednesday night in the Premier League.
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