Vazquez has spent his entire career with Los Blancos, but he could be on the move later this year after failing to negotiate a contract beyond June.
He is currently on wages of around £2.98 million annually and has reportedly declined to take a 10 percent pay-cut to extend his stay with the Spanish champions.
At 29, the Spaniard is eyeing a final big contract, and he looks set to pursue a free transfer away from Zinedine Zidane’s side this summer.
Vazquez is reportedly eyeing a four-year contract, and the aforementioned clubs are willing to meet his demands to land his signature.
Vazquez has not been a regular starter for Los Blancos over the years, but he has been a consistent performer on the playing field.
He can play on the right-wing or right-back and has most often played in the latter of those roles for Los Blancos this term.
He has managed a credible tally of two goals and seven assists in 31 matches, and his work rate is something that has been often talked about.
United have been on the search for a right winger for a while, and although Vazquez does not make regular scoring contributions, he could be an option for them.
His ability to play in the right-back position may be another attractive prospect, given Aaron Wan-Bissaka has offered limited threat going forward.
Chelsea have gone with Reece James and Callum Hudson-Odoi in the right wing-back role since Thomas Tuchel took charge as the manager in January.
The German may want signings of his own this summer, and Vazquez could be recruited to compete with James, as Hudson-Odoi is not accustomed to the position.
Stats from Transfermarkt.com