The north London club are eyeing a creative midfielder, and they have heavily been linked with the services of Leicester City’s James Maddison.
However, Romano has regularly emphasised that the Gunners are not close to landing the England international. Odegaard remains the priority for them.
Mikel Arteta’s side are prepared to sign the Norwegian on a permanent deal if Los Blancos give the go-ahead for the 22-year-old to leave the club.
Odegaard made a good impression on loan with the Gunners earlier this year, bagging two goals and two assists from 20 appearances.
He did not make a big impact in terms of goal contributions, but his clever movement and distribution helped them create more scoring chances.
Odegaard could only get better with consistent playing time over an entire campaign, and it remains to be seen whether the Gunners can re-sign him.
Leicester City’s James Maddison is valued at more than £70 million, and the Gunners seem reluctant to come close to meeting the price tag.
On the contrary, Odegaard could be available for around £42m, but a deal could be tricky with Los Blancos likely to demand a buy-back clause.
It would come as a surprise if Madrid sell him after it was recently confirmed that Toni Kroos has picked up a sports hernia injury.
Kroos is likely to be out for at least four weeks. Odegaard could get his chance to impress, having featured regularly during the pre-season campaign.
Stats from Transfermarkt.com