The Guardian is reporting that Chelsea FC have shown the most concrete interest in signing the highly-rated USA international.
The same article states that Liverpool FC and Tottenham Hotspur have previously been linked with a swoop to sign the 20-year-old.
According to the same story, Pulisic has refused to discuss a new contract with Dortmund despite his current deal being set to expire in 2020.
The Bundesliga side will be loathe to lose the promising American playmaker given his undoubted talent and growing prominence in European football.
Pulisic has emerged as one of the top players at Dortmund following the departures of Henrikh Mkhitaryan, Pierre-Emerick Aubameyang and Ilkay Gundogan in the past few seasons.
From a revenue perspective, the talented attacker would help BVB to tap into the lucrative American market as soccer continues to soar in popularity Stateside.
Pulisic is the standout talent in the United States national team after the Dortmund star made his debut for the USA at the age of 17 in 2016.
The Dortmund star has scored 15 times in 107 games over the past three seasons for the German club.
Pulisic could be a long-term replacement for Eden Hazard, whose current deal at the west London side is set to expire in 2020.
Roy Wegerle (1986-88): 15 appearances, three goals
Matt Miazga (2015-16): 2 appearances
Kyle Scott (2017-current): Currently on loan at Dutch club Telstar. Made Chelsea FC debut in 4-0 win over Hull City in FA Cup in February 2018.
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