The 26-year-old winger, who is a product of the Los Blancos academy, was one of Zinedine Zidane's most capped player last season, making 48 appearances where he scored eight goals and claimed 14 assists.
Although Vázquez is believed to be happy with life at the Santiago Bernabéu, Marcaclaim that at least three clubs in the Premier League are willing to give the former Espanyol forward a major pay rise to ditch Real Madrid this summer.
Chelseaare among Vázquez's suitors this summer, but domestic rivals Arsenal and Liverpool are ahead as the Blues continue to delay transfers until after they've appointed a new manager - believed to be Maurizio Sarri.
New Arsenal manager Unai Emery is reportedly keen on bringing his compatriot to the Emirates this summer due to his versatility and the Gunners will offer Vázquez a €3m pay rise to join the club. The north London side are also said to be tracking Portugal international Gelson Martins.
Milan were also believed to be keeping tabs on Vázquez this summer. However, their recent suspension from European competitions has dented their efforts, allowing neighbours Inter to steal the march on bringing the Spaniard to Serie A.
One sticking point for all of Vázquez's admirers is his hefty release clause in the Spanish capital. It is believed that clubs would have to pay €310m to activate the clause in his contract, something which would put all of the interested parties off of a deal.