Real Madrid are prepared to sell Martin Odegaard this month.
Goal says Arsenal are poised to swoop after they sold Joe Willock to Newcastle for £25m.
Carlo Ancelotti is set to leave the 22-year-old out Real's squad for their LaLiga opener against Alaves on Saturday.
His No 21 shirt was also given to Brazilian sensation Rodrygo.
And the club will now welcome any formal bid and will accept any of £34m and above. Arsenal initially signed the Norwegian on loan from Real Madrid in January.
He subsequently impressed boss Mikel Arteta, making 20 appearances and scoring key goals against Olympiacos and Tottenham.