Tuchel's comments come days after Manchester City boss Pep Guardiola claimed that "everyone" in England supported Juergen Klopp's Liverpool.
Chelsea said the new owners would pay 2.5 billion pounds to purchase shares.
Tuchel said their recruitment plans for next season are running behind schedule due to the uncertainty over the club's ownership, but added that the squad would require only "cosmetic surgery".
Third-placed Chelsea cannot afford another disappointing display this weekend as they try to move a step closer to sealing qualification for next season's Champions League.
Arsenal got off the mark when Eddie Nketiah pounced on a weak back pass by Christensen before slotting past goalkeeper Edouard Mendy in the 13th minute.
Christensen, reflecting on the first leg against Real, told Chelsea's website: "We have to try and turn it around but it's going to be difficult.
Chelsea were initially put up for sale by owner Roman Abramovich following Russia's invasion of Ukraine before sanctions were imposed on the oligarch by the British government, effectively giving it control of the club.
Holders Chelsea made light of their off-pitch problems to reach the Champions League quarter-finals.
Howe's side travel to Stamford Bridge on Sunday to face Chelsea, who will be playing their second game since the Russian billionaire's UK assets were frozen.
The Russian billionaire was one of seven oligarchs targeted Thursday by the UK government following Russia's invasion of Ukraine.
Sanctioned Chelsea Football Club owner Roman Abramovich cannot benefit from any sale of the club, Britain's minister in charge of sport, Nadine Dorries said.
Tuchel spoke warmly about the Russian's legacy at Chelsea.
Publicly at least, he remains calm and insisted the sale will not be a problem as his main focus remains on the players and his staff.
Abramovich announced on Saturday that he was giving "stewardship and care" of the club to trustees of the London side's foundation.
Tuchel's side took control of the tie thanks to Havertz's first-half header and Christian Pulisic's clinical finish after the break at Stamford Bridge.
Tuchel's side have won their last five games in all competitions, but there was little joy on the German's face when he reflected on Saturday's 1-0 victory at Crystal Palace.
Rudiger was struck by a lighter thrown from the away section during the second half of Chelsea's 2-0 win over their London rivals.
Tottenham battled hard in search of a route back into the tie but it was not to be their night
Conte stressed the importance of truthful communication with his players in the wake of Spurs' 2-0 defeat in the first leg of a League Cup semi-final against Chelsea.
Conte said Wednesday's 2-0 defeat at Chelsea in the first leg of their League Cup semi-final showed how far his current club lag behind his former one.