German giants Bayern Munich have also been monitoring the American winger during the last 18 months.
But the Bavarians, looking to overhaul an ageing side in 2019, have switched their attention from Pulisic to Bayer Leverkusen's Kai Havertz.
Bayern have all but dropped their interest in Pulisic; they reckon he would prefer to head to the Premier League and also that BVB would prefer to sell him abroad.
That is giving Premier League sides something of a free run at Pulisic who has just 18 months left on his deal at the Westfalenstadion and is available for the right price in January.