Mikel Arteta impressed by Odegaard at Arsenal and wants to keep him beyond the summer.
The Norwegian playmaker scored his first goal for the Gunners last Thursday.
Odegaard is currently on loan from Real Madrid and has made a withstanding impact at Arsenal in his last few games.
He has now scored two goals in his last two games.
Arsenal are keen on negotiating with Real Madrid to sign Odegaard either on another loan or sign him on a permanent deal.
There are chances of Real letting go of their Norwegian star as they would want to fund deals for Erling Haaland or Kylian Mbappe.
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Andy Cole told talkSPORT: “Odegaard is a baller. He’s technically very, very gifted.
“There’s talk of Arsenal trying to bring him to the Emirates [on a permanent deal] in the summer. I would be surprised.
“He’s had a few issues with Zidane. They’re not sure if Zidane will be there next season, so that’ll be interesting. The Arsenal fans love Odegaard.”