The Italian has told media in his homeland that the competition is a "prestigious trophy" and that "we want to honour it in the best way possible".
Ancelotti, who won the FA Cup as Chelsea manager in 2010, sees the trophy as one of the most achievable ways of securing European football for Everton for the first time since 2017.
The Toffees have won the cup on five previous occasions but have not made it past round four since their semi-final appearance five years ago. Last season, they were beaten 1-0 in the third round by local rivals Liverpool.
This is now a different-looking Everton side who have been transformed by Ancelotti since his arrival in December 2019; he has refined the club's existing talents such as Dominic Calvert-Lewin and Michael Keane, while adding quality in the shape of Allan, James Rodriguez and Abdoulaye Doucoure.
They currently sit seventh in the Premier League table – level on points with Tottenham Hotspur in fourth – with a 1-0 defeat to West Ham United on New Year's Day bringing an end to a four-game winning run.
Only Liverpool and Chelsea have scored more home goals than Everton in the top-flight this season, and their loss to the Hammers was only the second time they had drawn a blank at Goodison Park in the league.
It will be an uphill battle then for Rotherham, who are winless in their previous 10 away games – last claiming victory on the road on the opening day against Wycombe Wanderers.
The Millers have lost seven of their last nine games in the Championship, which has meant they have fallen into the relegation zone and three points adrift of safety; they do, however, have games in hand over the sides around them due to recent fixture postponements.
Manager Paul Warne had admitted that he is keen to "chew Carlo Ancelotti's ear off" after describing the Italian's book 'Quiet Leadership' as "the best book in sport".
Rotherham have very little FA Cup pedigree aside from a win over top-flight Southampton in 2002 and have never made it past the fifth round in their history. Last season, they avoided being on the wrong end of an upset in round two when they came from 3-0 down to win 4-3 against National League side Solihull Moors – scoring all of their goals in the final 15 minutes.
Saturday's game will be only the second meeting this century between Everton and Rotherham and only the 12th in total. Each of their last five encounters have come in the League Cup, most recently when the Toffees won 3-1 in 2018.
Everton form (FA Cup): LLLWLL
Everton form (all competitions): WWWLWL
Rotherham form (FA Cup): LLLWWL
Rotherham United form (all competitions): LLLWLL
Michael Smith's goal as a substitute in Rotherham's last game against Barnsley might encourage Warne to start the 29-year-old at Goodison Park.
Everton possible starting lineup:
Olsen; Kenny, Mina, Keane, Nkounkou; Davies, Doucoure; Gordon, Sigurdsson, Bernard; Tosun
Rotherham United possible starting lineup:
Johansson; Olosunde, Harding, Wood, Ihiekwe, Wiles; Crooks, Lindsay, Barlaser; Smith, Ladapo
We say: Everton 3-0 Rotherham United
Even if Everton do name a much-changed side, they are still likely to find this game fairly straightforward and the chance of an upset seems low. Rotherham are struggling for form and will see the cup only as a distraction from their relegation battle in the Championship.