Maddison signed a new four-year deal at Leicester worth about £100,000 a week last summer and contributed 14 goals in 16 matches between December and February.
The 24-year-old's contractual position and homegrown status mean Leicester would be in an extremely strong bargaining position.
They are thought to have rejected an offer from another club worth about £70m last summer, and Maddison described Leicester's FA Cup final win as the best day of his life, says the Daily Mail.
Arsenal believe there is still an opportunity to strike an agreement, with Gunners officials confident a package worth about £60m may get the deal done.
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