Giroud scored his 49th goal which is two goals off the top scorer record held by legendary Thierry Henry for France.
Rangnick will continue his consultancy role at the Old Trafford.
Italy made it a national record 31 games unbeaten as they edged past Austria in their Euro 2020 last-16 tie at Wembley Stadium.
It will be expected of Italy to create chances themselves and set the tempo of the match against Austrians.
Italy have history on-side heading into Saturday's last-16 tie with Austria, as Roberto Mancini's team aim to set new national records.
The Netherlands are through to the last 16 of Euro 2020 with a game to spare after a comfortable win over Austria.
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