The stopper was on loan at Bristol City this season after struggling for first-team football with The Foxes.
Leeds United's goalkeeping situation took another turn this week as the club lost yet more cover in the department.
USA Under-23 international Charlie Horton was signed by the club in the summer from Cardiff City but has left the club by mutual consent. The young talent is returning to the States because of a personal matter.
With Ross Turnbull out for the majority of the season with a broken ankle it leaves Italian Marco Silvestri as Leeds only main first-team option.
The club have the likes of Bailey Peacock-Farrell and Eric Grimes in support but, realistically, they need a more experienced option.
The 28-year-old has previously enjoyed spells in the Championship with Charlton Athletic but has played just 10 times for Leicester since joining the club in 2014.
This season he has already been given loan stints at Championship sides Nottingham Forest and Bristol City, although the former deal never officially happened due to Forest's transfer embargo, so Leeds know he is affordable and available for a temporary deal.
Of all the players in the Premier League Leeds could now target for the position, with the Anders Lindegaard option seemingly off the tale, Hamer represents their best opportunity.
He has two full seasons of experience in the Championship, is dying for an opportunity elsewhere after struggling at Bristol City and would provide real competition for the current Leeds United number one.