Allen shocked officials in the Treaty County earlier this week when he stepped down after two years in charge.
The Cork native this year led Limerick to the Munster title and the All-Ireland semi-finals, where they were beaten by Clare.
Sheedy won the 2010 All-Ireland with Tipperary, but work commitments forced him to quit the role.
He is currently 2/1 favourite with the bookies for the Limerick job.
