Milan came from behind to record a last-gasp 2-1 victory over Lazio in its previous outing, and remains two points clear at the top of Serie A after title rival Inter Milan lost its game in hand at Bologna on Thursday (AEST).
Stefano Pioli's team is unbeaten in 12 Serie A matches ahead of Sunday's meeting with Fiorentina (seven wins, five draws), but each of its past four fixtures of the campaign is against top-half opposition.
Giroud, whose only league title to date remains a shock Ligue 1 triumph with Montpellier in 2011-2012, says the Rossoneri are relishing being involved in an absorbing fight for the Scudetto, and insists being crowned champions of Italy would represent a "unique" achievement for Pioli's men.
"We're heading towards the end of the season and it's only normal that there's more pressure," Giroud said.
"But the group, the whole squad, is fully focused on the goal, which is to win the next game.
"Each and every player has to dream, think, eat and breathe to win the Scudetto, we're so close and everyone wants to win it, we can't hide from this fact.
"I hope this final run-in will be great for our fans, and I hope we will experience something unique, all together."
Giroud netted his ninth goal of the Serie A season in Milan's comeback win over Lazio, making this his best goalscoring league campaign since he scored 12 goals for Arsenal in the Premier League in 2016-2017.
France's 2018 FIFA World Cup winner has also scored more goals against Lazio than he has against any other opponent for Milan (three in two appearances), and said the dramatic nature of the victory made it "even better".
"We showed great team spirit, we never gave up and always believed we could win the game," he added.
"To win like this is even better, it's a great emotion in front of 10,000 Milan fans at the Stadio Olimpico. We played a good game and believed in the win until the end."
Milan is looking to secure the Serie A title off the back of a tremendous run of defensive form. Since the start of 2022 across the big five European leagues, only Liverpool (six) have conceded fewer than the eight goals shipped by Pioli's men in 15 league matches.