The news was first reported by Spanish TV station El Chiringuito and then picked up by Sport.
According to the reports, Ronaldo and Ramos handed in their requests to club president Florentino Perez in person.
If the rumours are to be true then one club who will be keenly interested are Manchester United.
The Premier League club have long hoped that Ronaldo would one day return to Old Trafford and were openly courting Ramos last summer.
It is believed by both news outlets that the pair have made the shock move to force a move away from the Bernabeu after defeat at the hands of city rivals Atletico last weekend.
The result left Real 12 points adrift of leaders Barcelona and third in the league, behind Atletico in second.
Neither the club or the players have so far commented on the reports.
