Wales international Koumas is wanted by Championship duo Birmingham City and Wrexham on a permanent transfer, says the Liverpool Echo.
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The forward spent last season on-loan in the second tier with Stoke City.
Norwich City, Preston North End and Hull City are also interested in Koumas before the September 1 deadline.
A move for Koumas is likely, with the youngster left out of Liverpool's Premier League 2 defeat to Leicester City on Monday night.