Spanish media outlet AS, as quoted by Daily Express, is reporting that Arsenal are in talks with the La Liga giants about signing the 28-year-old.
The same article states that Arsenal will have to cough up a transfer fee around £30m to sign the experienced midfielder this summer.
According to the same story, the Gunners will be able to conclude a deal in a swift manner if Arsenal are prepared to meet Real Madrid’s valuation.
The report goes on to add that the Europa League runners up could face competition from Paris Saint-Germain, Bayern Munich and Inter Milan for the winger.
The story adds that Vazquez is open to a move to Arsenal despite their lack of Champions League football for next season.
Unai Emery’s side finished in fifth place in the Premier League table last term to narrowly miss out on a Champions League spot.
Arsenal lost 4-1 to bitter rivals Chelsea FC in the Europa League final last season as Emery failed to win the competition for a fourth time.
The Gunners appointed Emery as Arsene Wenger’s replacement last summer after Arsenal finished in sixth spot in the table.
Brazil youngster Gabriel Martinelli signed for Arsenal last week.
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