The 26-year old is out of contract at Charlton Athletic next month and has not yet agreed a new deal with the Addicks.
The Foxes are eyeing a new gloveman as it becomes apparent that King Power Stadium number one Kasper Schmeichel is also yet to sign a new contract.
Leicester are preparing for life in the Premier League after winning the Championship title this season and are keen to reinforce their squad but face competition from West Bromwich Albion, Fulham and Burnley for his services.
Hamer has emerged as a target after establishing himself as one of the best young keepers outside the Premier League since joining Charlton from Reading in 2011.
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