The Blues sacked Tuchel last week after their 1-0 defeat against Dinamo Zagreb in their UEFA Champions League opener. They are sixth in the Premier League after winning three of their six games.
The club's new owners spent the highest amount among Europe's top five leagues in the summer transfer market, spending over £255 million on nine signings. However, that hasn't translated to success on the pitch so far for the Blues.
Chelsea have appointed former Brighton & Hove Albion manager Graham Potter as their new manager.
Arsenal, meanwhile, sit atop the Premier League standings, winning five of their six games. They have also strengthened this summer, having missed out on fourth spot last season by just two points to rivals Tottenham Hotspur. The Gunners will look to achieve that goal this season, having made a brilliant start.
Giroud, who has played for both London clubs, believes Arsenal could make the top four this season, telling Sky Sports (via HITC):
"Yes, definitely. I hope so.”
When asked about Tuchel's sacking, Giroud said:
“It’s part of football. It’s sad. I think Thomas (Tuchel) has done a great job for Chelsea and also watching my Gooners. I think it’s going to be another interesting year."
The Frenchman spent six years at Arsenal, registering 105 goals and 41 assists in 253 games across competitios. He move to Chelsea in 2018 and bagged 39 goals and 14 assists in 119 games.
Giroud now plies his trade for AC Milan, contributing 11 goals and four assists in 29 games in his debut campaign last season to help them to the Serie A title.
Arsenal and Chelsea's next fixtures
Premier League's Gameweek 7 was postponed due to the passing away of Her Majesty Queen Elizabeth II. Both London clubs will be in action in UEFA competitions this week.
Chelsea will face Red Bull Salzburg at home in the UEFA Champions League on Wednesday (September 14). Meanwhile, Arsenal will face PSV Eindhoven at home in the UEFA Europa League on Thursday (September 15).
If Gameweek 8 goes ahead, the Blues will face a struggling Liverpool side at Stamford Bridge on Sunday (September 18). Meanwhile, the Gunners will travel to face Brentford on the same day.
The gameweek will be followed by an international break before club football returns in October.