Shrews boss Paul Simpson told the club's website: "We agreed terms with the player and everything was okay.
"We agreed a fee with the club but in the end John O'Flynn decided not join any club other than those higher than League Two."
O'Flynn has scored 10 goals so far this season but has not scored since the start of December.
Simpson also revealed he had attempted to bring O'Flynn to the Prostar stadium last season to partner Grant Holt.
Shrewsbury had hoped to make a signing before the transfer window closed but the Town boss still hopes he can add to his squad before the end of the loan window.
O'Flynn joined Barnet from Cork in September 2008 and is out of contract at the end of the season.
Source: BBC Sport
