The Sun claims that the Wales international is high on Madrid’s list of transfer targets due his ability to play in a number of positions across midfield.
Madrid believe they are capable of persuading Ramsey to ditch the Gunners in favour of a switch to the Santiago Bernabeu, with Zinedine Zidane ready to offer the 25-year-old a chance of regular football.
Ramsey’s campaign has been disrupted by a hamstring injury and the midfielder has started just once in the Premier League this season.
Arsenal reportedly owe £11m from their Mesut Ozil deal, and this would be deducted in the fee Madrid would pay for Ramsey.
Madrid are appealing their transfer ban for the next two windows and are confident that they will win the case.