Chelsea have submitted a bid "north of €50 million" ($57m) to sign Christian Pulisic from Borussia Dortmund next summer, sources have told ESPN FC.

Bundesliga leaders Dortmund have ruled out selling the U.S. attacking midfielder in the January transfer window, but he will be allowed to leave the club in six months' time subject to an acceptable transfer fee.

Pulisic has assured the club he will not run down his existing contract, which expires in 2020, but Dortmund are aware he has his heart set on leaving Germany.

Chelsea are in pole position to win the race for the 20-year-old's signature with rival bids from the Premier League yet to emerge from Manchester United, Arsenal or Liverpool, and Dortmund are in no rush to conclude the deal in case counteroffers arrive.

United, who have expressed an interest in the player in the past, have not made any firm contact with BVB since Jose Mourinho's dismissal two weeks ago.

The feeling in Dortmund is that United will first attempt to find a long-term successor to caretaker manager Ole Gunnar Solskjaer before they turn to prospective transfer targets for next season.

ESPN FC has been told that Dortmund believe a rival bid might yet arrive from Arsenal, due to Pulisic's commercial value in the United States. The Gunners are controlled by Stan Kroenke, the owner of the Los Angeles Rams.

Bayern Munich have not ruled out a move for Pulisic either, sources have told ESPN FC. The Bavarians' prime target for next season is 19-year-old Bayer Leverkusen midfielder Kai Havertz, however, and Bayern have been informed that Pulisic would prefer going to the Premier League.

Sources told ESPN FC that Liverpool are no longer in the running. They tried to sign Pulisic in the summer of 2016 but had a €13m offer turned down for the player, who was 17 at the time.

The club currently do not have plans to sign a player in his position in upcoming transfer windows, ESPN FC has been told, unless circumstances significantly change.

Jurgen Klopp has Sadio Mane, Roberto Firmino and Mohamed Salah as his first-choice options in attack, with Xherdan Shaqiri adding depth and impressing following his £13m arrival in the summer.

All four players committed their futures to the club with long-term contracts in 2018. Sources said Liverpool are put off by the price it would take to sign Pulisic, a player they believe would not feature in their best starting XI.

ESPN FC's Liverpool correspondent Glenn Price contributed to this report.