The Foxes don't want to sell their talented playmaker and will make Arsenal pay premium if they want to pursue a deal.
Sky Sports says it will take around £70m for Leicester to even consider selling the 24-year-old.
Maddison is under contract until 2024.
The Norwegian enjoyed a successful loan spell in north London last season, but has expressed his desire to revisit his situation with Real.
But there are growing reports in Spain suggesting Real could allow him to leave with his contract due to expire in 2023.
Either way, Arsenal would need to sell players before pursuing either deal as both players would command significant fees.
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