The details are outlined by a report in Marca, who claim that the Spaniard is willing to stay at Los Blancos for the forthcoming campaign despite being told his current deal will not be renewed.
The 28-year-old had increasingly become a fringe figure in the Spanish capital last season, making just 18 in La Liga – of which just eight were in the starting line-up.
The adaptable Vazquez has won three successive Champions League titles and two La Liga crowns with Madrid since returning to the club from Espanyol in the summer of 2015.
Indeed, he has clocked up 206 first-team appearances across that spell but is finding himself increasingly surplus to requirements and Madrid will allow him to leave the club this summer if that is his desire.
However, it is increasingly likely that unless a new offer comes in that attracts him, he will stay in the Spanish capital for the final season of his contract.