Goal revealed on Saturday that Chelsea have been in talks with Dortmund over the United States international, with a £70 million ($89m) price tag being set.
The Blues have submitted a bid significantly lower than that asking price, while Pulisic is said to prefer a move to Liverpool.
Nevertheless, Sarri has refused to be drawn on the speculation, saying that to discuss a player he does not own would be improper.
"Pulisic is a Borussia Dortmund player and I don't want to talk about a player of another club," Sarri told reporters on Tuesday. "It's not professional, I think."
Alvaro Morata is a player who has been touted for a potential Chelsea exit given his unconvincing form over the past year.
Sarri wants to do all he can to help the Spain striker improve, however.
"I have to understand very well what he needs, but I am available to do everything," Sarri said.
"But I think that Morata, in the last month, played well. He scored five goals. He needs only continuity, I think.
"He needs confidence and confidence and confidence, so I think we need only to have continuity in the scoring.
"Now he is 26. He can change, but the characteristics of his character are this. So, he has only to stay calm because, in the last match, he missed the goal only because he wanted to score too much."