Asensio will miss the majority of the 2019-20 season after he ruptured knee ligaments against the Gunners on Wednesday.
According to Spanish publication AS, Los Blancos are reluctant to let any more players leave as a direct consequence of the winger’s injury.
Dani Ceballos is on the brink of joining Arsenal on a season-long loan in a deal which is still likely to go ahead.
Gunners boss Unai Emery also had designs on signing Real star Lucas Vazquez to bolster his options on the wing.
But in the wake of Asensio’s injury, the former Paris St-Germain manager will have to turn his attention elsewhere.
The breakdown in relations between Gareth Bale and Zinedine Zidane means Vazquez could have a major role to play this season.
The 28-year-old made 31 La Liga appearances last term but contributed just a solitary goal.
Zidane is prepared to let a number players go to ensure that Real met Financial Fair Play guidelines.
Alongside Bale, Mariano and James Rodriguez could potentially exit the Bernabeu to raise funds.
Meanwhile, reports in Spain suggest Asensio could be out for up to nine months with his knee injury
The star’s involvement at Euro 2020 could be in jeopardy if his country qualify for the finals.
A statement from Real Madrid said: “Asensio has been diagnosed with a rupture of the anterior cruciate ligament and the external meniscus of his left knee.
“The player will be surgically operated in the next few days.”
Arsenal lost to Real Madrid on penalties last night after throwing away a two-goal lead.
Alexandre Lacazette and Pierre-Emerick Aubameyang scored for the Gunners, Bale the pulled a goal back before Asensio scored the equaliser in the 59th minute.
The north Londoners still top of the International Champions Cup table with two wins from their three games.