Chelsea sacked Tuchel on Wednesday, a day after the London club suffered a shock 1-0 defeat at Dinamo Zagreb in their Champions League opener.
When asked if he would ever get a haircut to avoid a similar fate in the future, Cucurella grinned and told reporters: "No, no, never! This is my style."
Tuchel's comments come days after Manchester City boss Pep Guardiola claimed that "everyone" in England supported Juergen Klopp's Liverpool.
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.
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.
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.
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.
Lukaku's comments about being dissatisfied with life at the club are unhelpful, manager Thomas Tuchel said on Friday.
Pulisic suffered an ankle injury while playing for the United States during the international break last month.
When Chelsea triumphed in Porto against Pep Guardiola's team in May, the result was considered an upset with City heavily backed to win their first Champions League.
Chelsea have extended Thomas Tuchel's contract until 2024 after the German manager won the Champions League this season, the London club said on Friday.
Tuchel is seeking his first Champions League title, after losing out to Bayern Munich with Paris Saint Germain in last season’s final.
In-form Chelsea will fancy their chances at Wembley in a match that could serve as a dress rehearsal for the Champions League final.
Tuchel praised his side for overcoming the shock of last week’s 5-2 defeat to West Bromwich Albion as they beat Porto 2-0 in Wednesday.