Arsenal has been used to signing players from Real Madrid since Mikel Arteta became their manager.
The Gunners had Dani Ceballos and Martin Odegaard in their squad on loan from the Spanish club last season.
They have since made the transfer of the latter permanent after they enjoyed his performances for them in his short loan stint.
The Gunners expect to have started this campaign brightly after they missed out on European football last season.
But they have started with three league losses from as many games with Mikel Arteta now under serious pressure.
The transfer window has just a few more days before it finally closes and the Spanish boss could bring in a few players still.
Transfermarketweb reports that they are now looking to sign Marco Asensio from Madrid.
The Spaniard is an exciting player to watch, but he has been hampered by persistent injuries in recent seasons and he is not a part of the plans of Carlo Ancelotti.
The report says he is now considering leaving the club and the Gunners want to add him to their squad in this transfer window.
It says Tottenham and Liverpool also want to sign him, but Arsenal is his most serious suitor.
Arteta hopes the club will make a move for him and Madrid values him at £34m.