The Gunners have not won the FA Cup since the 2-1 victory over Chelsea in 2020, a final that was played behind closed doors due to the COVID-19 pandemic.
Furthermore, Mikel Arteta's side has failed to progress past the fourth round for five successive seasons since the FA Cup title triumph.
"Today it's a change of focus in the FA Cup, which is a big target for us," said Odegaard to the club website.
"This group of players hasn't had a run in this competition, and it's definitely something we want to do. We know we can do better in this competition. In recent years, we've gone out quite early, so that's something we want to make better and it's another competition we want to go all the way in."
The Norwegian midfielder is wary of being overconfident ahead of the fixture against lower division opponents and has urged his side to remain focused for the match.
"We are in strong positions, and we will keep focused on ourselves and pushing in all competitions, added the 27-year-old.
"Facing a team from League One means we have to stay completely focused, because for them it's kind of like a free hit."
Arsenal will be looking to add to their record 14 FA Cup titles while attempting to win a quadruple of competitions this season.
Mikel Arteta has delivered an impassioned rallying cry to his Arsenal squad, insisting they must play with "no fear" and "pure fire" as they enter a decisive week that could shape their season.
Virgil van Dijk has delivered a clear message ahead of a defining night for Liverpool FC - believe, fight, and embrace the moment.
Luis Enrique has warned his Paris Saint-Germain side to stay fully focused as they prepare to face Liverpool tonight at Anfield in the Champions League quarter-final second leg.
Manchester United head coach Michael Carrick has launched a furious defence of Lisandro Martinez after a controversial red card overshadowed a 2-1 defeat to Leeds United at Old Trafford on Monday night.
