Manager Danny Wilson told BBC Radio Sheffield: "There are a few clubs who have been after him.
"He has pace and offers us a wide position and ability to get into spaces and score goals."
Flynn started his career at Falkirk before moving to Liverpool as a teenager in 2005 for a fee of ?50,000. He was a member of the Liverpool youth team that won successive FA Youth club titles in 2006 and 2007 before returning north of the border to rejoin the Bairns in 2009.
Flynn scored Falkirk's first ever European goal in the 1-0 win over Liechtenstein side Vaduz.
Source: BBC Sport
Source: BBC Sport