The two clubs have already entered into talks over the deal and according to AS, there is genuine hope negotiations can be concluded as early as next week.
Vazquez is keen on a move to the Premier League and is desperate for regular first-team football in order to win a place in Spain's Euro 2020 squad.
With Real Madrid signing Eden Hazard and Luka Jovic, the 28-year-old is likely to be condemned to the bench if he stays in the Spanish capital.
Zinedine Zidane's side also need to raise funds for other big-money moves.
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Inter Milan, Bayern Munich and Paris Saint-Germain are also interested in Vazquez, but Arsenal are currently winning the race.
Zidane has spoke with the player and the Spaniard reportedly told the Frenchman that a move to the Gunners is the best way to achieve his current goals.
The deal overall would cost Arsenal an initial fee of £28.7m, with £2.7m to come in add-ons.
That is less than half of the £80m fee quoted by Crystal Palace to sign Wilfried Zaha this summer.
If the Gunners' budget really is as strict as it has been quoted in the media, signing Vazquez would be a no-brainer.
He was a key member of Zidane's Champions League winning sides, but he didn't enjoy his best season in 2018/19.
In his 31 La Liga appearances - of which he only started just 15 - he managed just one goal and three assists.
However, his skillset could be invaluable to Arsenal right now.
His passing, dribbling and defensive contribution from out wide are things the Gunners sorely miss at the moment.
And at the age of 28, he should be approaching his peak years.
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