Vazquez, 29, who will miss Euro 2020 due to an anterior cruciate ligament tear joined Madrid from Espanyol six years ago.
According to media reports Vazquez had offers from Bayern Munich and other European clubs but chose to stay on under newly-appointed coach Carlo Ancelotti.
Vazquez, who was moved from his usual position on the right wing by former boss Zinedine Zidane, is likely to return from injury for the new La Liga season.
Club captain Sergio Ramos' contract is also up at the end of this month.
Source: www.beinsports.com