Ramos, 35, called it time on a legendary career at Madrid this summer and completed a sensational free transfer to Paris Saint-Germain.
Varane, meanwhile, is on the verge of leaving Los Blancos after Manchester United announced they had reached an agreement for his transfer.
Marcelo succeeded Ramos as club captain earlier this month, saying it was an "honour and an enormous responsibility to be captain" of Madrid.
According to Football Espana, Madrid striker Karim Benzema will serve in Marcelo's absence as the club's second captain.
Nacho has reportedly been named as the club's third captain, while Varane was initially going to be the fourth ahead of his move to Old Trafford.
Mundo Deportivo now reports that long-standing Madrid midfielder Luka Modric will now take the soon-to-be United player's place as Los Blancos' fourth captain.
Football Espana added that the 35-year-old Croatia captain is 'very much a senior figure in the dressing room.'
United splashed out an initial fee of around £34m to sign Varane, which could rise to £42m with add-ons.
Varane, whose Madrid deal expired next summer, will complete his move to United after his medical and official contract signing.
The 28-year-old French centre-back was tipped as a potential candidate to replace former teammate Ramos as Madrid captain.
Ramos took to Instagram and sent Varane a touching message, saying that the outgoing Madrid star's next chapter at United "will surely be exciting."
The former Los Blancos skipper wrote: "Dear Rapha, I can only thank you for these years of friendship, companionship and triumphs, and wish you luck in a new stage that will surely be exciting.
"If we face each other, always with the team of your country, right? Take care."
Featured Image Credit: PA
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