Blues boss Maurizio Sarri seems to have beaten several Premier league clubs, including Liverpool, Arsenal and Manchester United, in capturing the signature of the 20-year-old.
It seems likely that the American’s desire to play in the Premier League will come true with Chelsea confident a deal can be completed.
However, any agreement is unlikely to see the player move in the January window as Dortmund want him to see out this season in the Bundesliga, and so the move is expected to occur in the summer.
A further confirmation that a deal is about to be announced, came in the form of a social media post from American striker Eddie Johnson.
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The former Fulham, Cardiff and Preston forward posted picture of Pulisic in a half Dortmund and Chelsea kit.
“So stoked for you lil’ bro, great move,” Johnson wrote.
“Can’t wait to watch you alongside Eden Hazard.”
Although Chelsea fans might have to wait a few more months to see Pulisic sign, they can still expect some activity in the January transfer window.
Sarri is reportedly looking to bring in reinforcements at the back, as the future of David Luiz at the club remains unresolved.
The Brazilian defender’s contract will expires in five months and no agreement has yet been agreed over an extension.
However, fellow compatriot Willian is keen for the ex-PSG star to remain at Stamford Bridge.
“David has a lot of quality to do these kind of passes,” Willian said.
“Of course. I want him to stay. We have to see if the club will want him.
“I think they want him. For me, I want him to stay.”
Chelsea face Southampton on Wednesday and a victory at home will open up a five-point gap to fifth placed Arsenal.
The Blues are currently 11 points of Premier League leaders Liverpool, who play Manchester City on Thursday.