The Gunners beat Burnley on Monday night to move within one game of winning the league as they prepare to clinch the title with a win over Crystal Palace this weekend.
Manchester City must now beat Bournemouth at the Vitality Stadium on Tuesday night to take the championship race to the final day of the season and if they fail to win, Arsenal will be crowned champions early.
Arsenal, who have finished as league runners-up for the past three seasons, also have the chance to become European champions as they face Paris Saint-Germain in the Champions League final later this month.
Speaking after the Burnley clash, Odegaard revealed that his side have trophy fever and hope to bring at least one piece of silverware back to North London.
“I am really proud. It has been an amazing season so far. We have one big one left and then the Champions League final and we want to take the trophies home.
“I can promise you all that we will give everything we have, and keep going until the very end and with your support we are going to be ready.”
All eyes now turn to City’s clash with Bournemouth on Tuesday night as Arsenal hope their title rivals do not continue their perfect run, allowing Arsenal to collect their first piece of silverware on the way to a double.