The party’s Cork North Central branch will decide this evening on who to put forward at its selection convention.
Mr Murphy, who was controversially driven by two gardaí from rural Cork to Dublin Airport earlier this month after his car broke down on the motorway, is facing stiff competition from Fine Gael senator Colm Burke for the nomination in the four-seat constituency.
While the government party has yet to clarify whether it will run one or two candidates, a recent leaked Labour poll showed its coalition partner will win just one seat, with Mr Murphy and Mr Burke tied for support .
When contacted over the controversy surrounding his party colleague and rival last Friday, Mr Burke said he was not “fully aware of the facts” and did not wish to comment.
Local rivals Labour junior minister Kathleen Lynch, Fianna Fáil health spokesperson Billy Kelleher, and Sinn Féin’s Jonathan O’Brien are all expected to retain their seats, meaning a two-candidate Fine Gael strategy is unlikely.
While Fine Gael ran two candidates in the constituency in each of the last four general elections, its support has dropped from obtaining the first two seats in the then five-seater area in 1997 to winning the final seat and finishing just outside the Dáil positions in 2011.
Meanwhile, two other high-profile selection conventions also take place tonight.
Fine Gael is likely to decide to run Agriculture Minister Simon Coveney and health committee chair Jerry Buttimer in Cork South Central — an area that also contains Fianna Fáil leader Micheál Martin, finance spokesperson Michael McGrath and Labour’s Ciarán Lynch and has been reduced from five to four seats. In Dún Laoghaire, Fianna Fáil faces a far more difficult decision.
Grassroots members will this evening choose one of councillors Kate Feeney, Mary Hanafin, and Cormac Devlin to run in the four-seat area — only three of which are available as ceann comhairle Seán Barret will be automatically re-elected.
Ms Hanafin or Ms Feeney are believed to be headquarter’s preferred candidates, despite polls conducted by Mr Devlin’s officials claiming he would win the internal convention vote.
Separately, Dublin South West Labour TD Eamonn Moloney has stepped down from the party and will instead contest the general election as an independent. He previously hit out at Labour headquarters for deciding to run two candidates in the area.