The Blues are pressing ahead with transfer plans, despite their current ban on signing players, with a Court of Arbitration for Sport [CAS] appeal verdict due any day, and are willing to pay more than the £72 million they stumped up to capture goalkeeper Kepa Arrizabalaga from Athletic Club last year, goal.com reported.
Sancho enjoys a close relationship with a number of Chelsea players, including England teammates Tammy Abraham and Callum Hudson-Odoi, and hails from London.
He is understood to be ready to leave Dortmund after enduring a turbulent start to the Bundesliga season as, although Sancho's output has remained high, he has been hit with disciplinary sanctions this term.
The 19-year-old was pulled from a league match against Bayern Munich after only 36 minutes, with coach Lucien Favre slamming the player as "not good enough" and last week Sancho was dropped from the starting lineup to face Barcelona in the Champions League after reporting late for a pre-game team meeting. Favre said after the game that he needed "focused players" for the fixture, which Dortmund lost 3-1.
Those issues have helped to signal hope that Dortmund may consider selling its number one asset sooner rather than later, with moves for Antony of Sao Paulo or Everton of Gremio in the works and to be funded by using any proceeds from a Sancho departure.
Dortmund sold Ousmane Dembele to Barcelona for an initial €105 million in 2017 and Sancho would likely command a fee above that figure given his current contract runs until 2022.
Liverpool is known to be admirer of the England forward but manager Jurgen Klopp has admitted that the price is too high. The European champion would also have no space for Sancho in its starting lineup as long as Sadio Mane and Mohamed Salah remain at the club.
For its part, United is prepared to pay up to €140 million (£119 million/$155 million) to land Sancho in January but is hampered by the fact that it is a long way from the Champions League places Chelsea currently occupies.
Moreover, Chelsea’s wide forwards Willian and Pedro are out of contract at Stamford Bridge next summer with space opening up for a new player in that position.
Manchester City, the club Sancho left in order to move to Dortmund, is not currently interested in re-signing its former player.