Boss Arsene Wenger has a ?70m war chest and has accepted he needs to bring in top talent following an eighth successive season without a trophy.
While the Gunners were going out of the Champions League on Wednesday, the attacking midfielder, 20, was scoring the crucial first goal as Malaga beat Porto 2-0 at home, reaching the last eight 2-1 on aggregate.
Isco, full name Francisco Roman Alarcon Suarez, is seen as one of the hottest young players in the world.
He made his full international debut for world and European champions Spain last month, playing the last 30 minutes of a 3-1 win over Uruguay.
Arsenal are likely to face stiff competition for Isco?s signature, but chief scout Steve Rowley has been following his progress for some time.
The Gunners also have an advantage in that they have already done business with Malaga, signing left-back Nacho Monreal in January for ?6m, and initial talks have been held about a deal for Isco.
Monreal has given Arsenal a glowing report about Isco?s suitability for the fifth-placed Gunners, who now face a battle to qualify for next season?s Champions League.
They impressed many with their 2-0 win at Bayern Munich, which saw them draw 3-3 on aggregate but go out on away goals.
Keeper Lukasz Fabianski looks certain to keep his place for the trip to Swansea tomorrow, having replaced dropped Wojciech Szczesny, who did not even travel to Germany.
Mikel Arteta, who skippered Arsenal in place of the axed Thomas Vermaelen, said he was keen for Fab-ianski to be given a run in the team.
?I would hope so,? said the midfielder. ?He did it against Bayern, so why can?t he do it in the following games? He was terrific mentally as there was a lot of pressure on him. He came in and was fantastic.?
Source: DSG
Source: DSG