The Gunners extended their lead at the top of the table to eight points after beating Crystal Palace 4-1 at the Emirates on Sunday.
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Mikel Arteta's side have already matched last season's tally of 69 points with ten games to go.
The north Londoners have won six consecutive top-flight matches for the first time under the tutelage of the Spaniard.
Fans are now finally starting to believe that they could end their 19-year wait for a title.
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And captain Odegaard, who has chipped in with ten goals and seven assists in the league this season, has now admitted that he too is thinking of winning the championship.
Speaking to talkSPORT's chief football correspondent Alex Crook, Odegaard was asked whether he is dreaming of lifting the Premier League trophy.
To which he said: "Yeah, you can always dream!
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"It's been my dream since I was a baby, so of course you can dream.
"But the main thing is to stay calm, to keep working hard and to keep pushing every day to make sure that we get better every day."
And the Norway international has declared the players are thriving of the pressure of being in a title race against defending champions Manchester City.
He stated: "I think everyone enjoys it, we are where we want to be.We have to enjoy it.
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"We are in a good position, so we want to enjoy this, and the connection with the fans, within the team, everyone is so together now.
"So we just have to keep going the same way and keep pushing every day to get better and to stay where we are."
Arsenal's win over Palace was even more impressive considering the fact they were dumped out of the Europa League on Thursday night against Sporting Lisbon after losing on penalties.
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Pressed on how the club continue to bounce back emphatically after suffering setbacks, Odegaard remarked: "I think it just shows that we are a group of hungry players.
"I think Thursday night was a bit tough for everyone, we wanted to do something special in the Europa.
"It was a long night as well, extra-time and all that, so it was a tough one to take, but we came in the next day and wanted to bounce back, so everyone was ready [against Palace], and that's what we did."