The Telegraph says Leicester are looking at the 24-year-old for the summer market.
The Foxes see Sanchez as a potential replacement for Kasper Schmeichel who is rumoured to be leaving.
The Dane is a target for Newcastle United.
Sánchez, 24, moved to Brighton's academy in the summer of 2013, when he was 16 years old. He is now a regular with Spain.
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