Potter was fired on Sunday after his disastrous reign as manager of Brighton ended with a humiliating home defeat against Aston Villa.
Chelsea is looking for their third permanent manager of the season, with Potter hired in September following the surprise dismissal of Thomas Tuchel.
Meanwhile, Bruno Saltor, a member of Potter’s backroom staff, took over as Chelsea interim manager.
Chelsea remain 11th, leaving them with an uncertain future despite Chelsea owner Todd Boehly’s massive investment in new signings since taking over last year.
Liverpool hardly looked much better as a third successive league game without a win damaged their faint hopes of finishing in the top four.
Eighth-placed Liverpool are seven points behind fourth-placed Tottenham in the race to qualify for the Champions League.
Chelsea and Liverpool finished in the top four and met in the FA Cup and League Cup finals last season, yet less than a year later they are languishing in mid-table amid turbulent campaigns.
In response to Liverpool’s dismal 4-1 defeat at Manchester City on Saturday, Klopp dropped Mohamed Salah and Trent Alexander-Arnold as the Reds boss made six changes.
It was Chelsea who made the stronger start of the two troubled teams and Mateo Kovacic’s shot was blocked on the line by Ibrahima Konate.
Reece James saw his fierce finish disallowed for offside against Enzo Fernandez, while Wesley Fofana was narrowly off target with a headed chance.
As in the other Premier League games on Tuesday, there was a first-half pause at the Bridge for Muslim players to break their Ramadan fast.
Chelsea’s Kai Havertz dragged a good chance wide from N’Golo Kante’s pass immediately after the restart.
Darwin Nunez and Joe Gomez forced good saves from Kepa Arrizabalaga as Liverpool finally threatened just before half-time.
Kovacic blazed a glorious chance over soon after the interval, while Havertz’s effort was disallowed for handball when the German’s shot hit Liverpool keeper Alisson Becker and rebounded into the net off his arm.
Leicester’s first game since Brendan Rodgers’ departure on Sunday ended in a 2-1 defeat against Aston Villa at the King Power Stadium.
The Foxes, led by caretaker bosses Mike Stowell and Adam Sadler after Rodgers’ exit by “mutual agreement”, have now gone seven league games without a win and sit second bottom of the table.
Ollie Watkins put Villa ahead in the 24th minute and although Harvey Barnes equalised after 35 minutes, Leicester’s Kiernan Dewsbury-Hall was sent off in the 70th minute for a second booking.
Bertrand Traore’s 87th-minute curler, his first goal for Villa since 2021, piled on the misery for Leicester.
Leeds climbed out of the relegation zone with a 2-1 win against fellow strugglers Nottingham Forest at Elland Road.
Orel Mangala bagged his first goal in English football to fire Forest ahead.
But Jack Harrison equalised eight minutes later with a close-range finish after Keylor Navas spilled Marc Roca’s shot.
Luis Sinisterra put Leeds in front in first-half stoppage time, cutting inside and curling his shot into the far corner.
Leeds are two points clear of the relegation zone, while Forest are outside the bottom three on goal difference.
Third-bottom Bournemouth remain in deep trouble after a 2-0 home defeat against Brighton.
Albion took the lead in the 28th minute through teenage forward Evan Ferguson’s audacious backheel, with Julio Enciso’s first goal for the club wrapping up the points in injury time.