Kilbeggan's Kate O'Connell has emerged as a contender to replace him.
Former Fine Gael Minister Eoghan Murphy has resigned his seat in the Dáil.
He served as Housing Minister in the last government having first been elected as a TD in 2011.
Eoghan Murphy's now-vacant seat in Dublin Bay South will have to be filled within 6 months and it's already shaping up to be a fascinating battle.
At first glance it would seem former Fine Gael TD, Kilbeggan's Kate O'Connell is the natural successor.
Relations between her and Leo Varadkar are frosty with the Fine Gael leader snubbing her twice for a Seanad nomination and O'Connell remarks from his leadership elections when she branded his supporters choirboys not forgotten.
Local councillor James Geoghegan has been mentioned as a potential Fine Gael candidate.
MEP Frances Fitzgerald has ruled herself out despite WhatsApp Group rumours this morning.
A similar headache in the Green Party - Dublin Bay South is the patch of Dublin's Lord Mayor Hazel Chu.
It's also party leader Eamon Ryan's constituency - and the two have been at odds over Chu's solo-run for the Seanad as an Independent.
There's plenty of speculation that were Kate O'Connell or Hazel Chu not to get the nominations of their parties they may contest the election as Independents.
Divisions could also be highlighted in Fianna Fáil if Micheál Martin picks a candidate to contest the by-election in potential future party leader Jim O'Callaghan's constituency.
Sinn Féin will likely use the election as a test of its strong polling, with Senator Lynn Boylan mentioned as a possible runner.
Labour expect to field well known Senator Ivana Bacik as a candidate.
While eyes will also turn to former TDs Michael McDowell and Lucinda Creighton and whether they would consider a run.