The Gunners completed a deal to take Odegaard on loan from Real Madrid until the end of the season on Wednesday, handing the attacking midfielder the number 11 shirt that was worn by Mesut Ozil when he joined the club.
Odegaard was signed by Los Blancos from Stromsgodset as a prodigious teenager and has had loan spells in the Eredivisie with Heerenveen and Vitesse before impressing in a temporary stint with Real Sociedad last term.
Madrid opted to recall him for the 2020-21 campaign, though the 22-year-old struggled to nail down a regular spot in Zinedine Zidane's team.
Arteta is excited by Odegaard's qualities but did urge caution, saying comparisons to Barcelona great Messi are unhelpful.
"I wouldn't even get close to that name you just mentioned [Messi] because it's a lost battle in my opinion. Martin is Martin," Arteta said when previewing Saturday's clash with Manchester United.
"In the last few seasons he's progressed and developed in the right way. I follow him very closely because he played for Real Sociedad which is my hometown and I know him really well.
"He's such a talent. He needs the right environment, a little bit of time, but he's got the qualities to be a success for us. He's a specialist to playing in the pockets, to be in the number eight, number 10 positions.
"He can play on the sides, a really creative player, really comfortable on the ball in tight spaces, the capacity to create chances, to score goals.
"Something he has improved a lot is his work rate without the ball as well. It's another option to give us more creativity in the final third."
Last season, Odegaard topped Sociedad's squad for chances created in LaLiga, crafting 62 opportunities in total as he provided six assists from 31 appearances. He also boasted an impressive passing accuracy of 84.74 per cent.
This term he has been afforded just three LaLiga starts by Zidane, albeit Arteta made clear several factors will determine whether a permanent deal will be struck.
"He has certainly all the qualities and characteristics that we are looking for," he added.
"Then it would be down to two things – first of all, how well he adapts here and how much of an impact he can have in our team, and second, what Real Madrid and the player thinks about it because he's owned by Real Madrid and the player has a big say on that.
"I just wanted to give him a clear picture of who we are as a club, what we are trying to do, what we expect from him, just try to transmit the passion and excitement that we had to bring him in.
"I wanted to show him the project, how he fits and just try to persuade him that this is the right place for him and try to make things work."
Arsenal are on a six-match unbeaten run in the Premier League to improve their previously precarious top-flight standing to ninth.
They welcome a Manchester United side who saw their own 13-match unbeaten league run surprisingly ended by rock-bottom Sheffield United on Wednesday.
"It's not a surprise because to beat any team in this league is extremely difficult and it's not taken for granted," Arteta said when asked about that game.
"Sheffield United are a really good threat and you see that. They've lost games they didn't deserve to lose."
Arsenal were the last side to beat United in the league before the Blades' unlikely triumph, while they have not lost to the Red Devils since an FA Cup defeat in January 2019.
Still, Arteta says there is nothing to be gleaned from a decent recent record against United.
"I think every game is completely different, they have the capacity and the quality to beat any side in the world, we know we’re going to have to be at our best," he said.
"The games are huge, we need to be better than what we were on Tuesday [a 3-1 win at Southampton] to beat them.
"They've been in top form. They've been top of the table playing really well. We know they are a real threat. We have to be at our best to beat them on Saturday."