The former Charlton man played a bit part role on Merseyside last season and is set to see him playing time limited further as new additions are set to arrive at Liverpool this summer.
The Reds are keen for a permanent deal to be done, freeing up some extra funds for Rodgers to invest in the squad.
Shelvey’s boyhood club West Ham are one of a number of Premier League sides interested in the midfielder and the England under-21 international would relish playing for the team he supports.
Liverpool are set to wait until Luis Suarez’s future is dealt with before letting other attacking players leave.
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